To the answer by u/Dicranurus, I would add a few details.

• Tourist trips abroad did exist, but their likelihood only reached a non-zero amount if you were a government worker with good set of perks (or acquaintances / connections), and they were organized entirely for you in an official manner. Importantly, such a tour would only target a "friendly" country, either of the Socialist bloc, or a currently USSR-aligned country — such as Cuba. As an anecdotal example, my adoptive grandfather, an army colonel and a "district military comissar" (this lofty title just meant he was in charge of the local town/disctrict recruitment station) did get a fully paid vacation to India, which he and his wife cherished for years afterwards.

• Still, if you asked anyone you knew (or yourself) who are the Soviet people who can go "abroad" (truly abroad, to Western countries — as the joke went, "chicken is not a bird, and Poland is not abroad"), the firm answer would be "diplomatic corps". Only those working in embassies and in related services enjoyed regular trips to other countries and greatly relaxed allowances to transport and own foreign goods for personal use (...and for some light under-the-table profiteering). This is the reason that Foreign Relations Institute (MGIMO) and similar uni departments still have a mystical aura of extreme prestige in Russia, esp. for older folk.

• Now, the currency. The problem of expense basically started and ended with the important fact that Soviet rubles were officially NOT a convertible currency (only exchanged by authorities for international trade or government business*... or illegally, on the pain of severe criminal persecution). It was not necessarily a function of a Soviet citizen being poor; in fact, the official exchange rate for, say, dollars was so favorable that a Soviet engineer could take a fair amount of dollars on vacation... if anyone'd let him. In reality, foreign convertible currency was a controlled good, and was illegal to possess without authorisation. There even existed ["Beryozka"](https://en.wikipedia.org/wiki/Beryozka_(Russian_retail_store)), a chain of "foreign currency stores" which catered to foreign visitors, but also were designed for diplomats to spend their leftover currency or diplomatic cheques in a legal manner, to buy high-quality grocery and products.

• Internal migration inside USSR (NOT between Warsaw pact countries!) was relatively straightforward as long as it was a work transfer. In that case, the relocations would be more or less assisted, and you would receive housing (either temporary worker housing, or a proper apartment, depending on the contract and your qualifications) immediately, or a chance to be eligible for an apartment after a set number of years (basically a preference in the queue, see below). A good example would again be officers, who often moved house every few years, and received a new issued apartment or dormitory room (if an "officer's house" wasn't yet completed) each time.

• Spontaneous migration was possible, but more difficult, and fundamentally was the same as work migration. You'd still have to look for a job (having a job for an able citizen was mandatory), again with accompanying housing benefits — at least a spot in a worker dormitory. So it's not that different — either you look for a job beforehand, or look for a job after arriving.

• NOTE: If you graduated from a university, the work distribution program (basically something like guaranteed employment with a set number of years to "work off" the education) would actually make it quite likely that you'd be offered job and housing in a completely different place of the country (often a remote one, with a shortage of specialists), and would have to move. This sudden move could be bothersome, but would also promise the graduate guaranteed personal housing, a change of scenery, and maybe good benefits — remote locations had multiplicative salary bonuses.

• If you wanted to just move some of your relatives right now (as in your example), you'd probably have to make space, and endure a little bit of cramped living. Your sister would have to try and resolve this housing problem, living at your place in the meantime. On the other hand, no one would prevent them from moving in with you! Waiting in line for issued apartments, having to share rooms with older or younger relatives, living with distant relatives for a while, exchanging, splitting, and "merging" family apartments (e. g. exchanging two smaller ones for a big one, or a big one for two smaller ones) were all realities of late Soviet family life. In theory, each citizen was eligible for certain apartment space, which placed them on a waiting list as apartments are being built; but this was an ongoing process even as USSR ceased to exist in 1991. Housing in USSR never quite reached the goal "an apartment for every nuclear family", without waiting lists or favoritism; but it was gradually going in that direction. With that said, 1960s (as the time when the acute housing crisis has just STARTED being resolved) would see a lot of noisy, crowded three-generation small apartments, and similarly crowded communal apartments (several apts sharing kitchen and bathroom). Also, standalone single-family houses were a thing (both in villages, and in town suburbs), but were far less prevalent and mass-built than in US.

• Now, about passports. Everyone has a passport! But it's the domestic Soviet passport — your universal ID that also lists your children, your marriage, your registered place of residence, military draft status, conviction history, and other marks. Quite importantly, collective farm workers and non-specialist peasant villagers, at the time period of your question, did not have a passport and were tied to their place of residence, at the discretion of their employers (even after 1976, their passports were stored at their administrator's and could be withheld if desired). But adult urban dwellers just had it as a default, and could buy a ticket to go anywhere inside USSR at any time. And train/plane tickets were actually quite affordable. In fact, internal tourism was a rather mundane activity and a preferred way of spending one's vacation for people with medium-level income and above.

• As for international passports, there was a whole variety of 'em (citizen international passport, diplomatic passport, service passport...) but this point is rather moot, because as noted above, you only go abroad as an official tourist group or on a work trip.

• Finally, a small nitpick: your sister probably wouldn't be able to move to Stalingrad specifically, since it was renamed Volgograd (after Volga river) following the denouncement of Stalin's cult of personality in 1956; the renaming was finalized in 1961.

* It's a complicated mire of special parallel currencies, "foreign trading bank cheques", travel cheques... Suffice it to say that normal internal rouble that people bought stuff with inside USSR was a closed currency, and could not be exchanged by anyone bar the foreign trade ministry.

As an average Soviet citizen, you simply couldn't travel abroad. The process of obtaining permission was very protracted, the trip itself very expensive, and (especially for capitalist countries) brought unwanted scrutiny. The most likely way an 'average' citizen would leave the Soviet Union or have an employer/union-sponsored trip was through trade unions, where you could visit places like Sevastopol or, rarely, go abroad. Trips outside the USSR were just not a realistic option for most Soviet citizens; migration within the USSR was more likely, but not without its own difficulties. You will most likely be left to enjoy Western culture through media that filters through (especially post-1956), but in a uniquely Soviet way - Gilburd's To See Paris and Die explores how Western culture was reinterpreted in the Soviet Union.

As for internal migration from Kiev to Volgograd, it was certainly possible, but difficult. But if you can secure sponsorship in Volgograd you're likely able to, as Kiev is a larger, more desirable city (to immigrate from Volgograd to Moscow would be more challenging, depending on your qualifications). If you were willing to live in quite poor conditions you could likely emigrate as an industrial worker, but with hindsight it's worth mentioning that the apartment you would receive would be absurdly taxed right around the time you could move out of the migrant housing!

There's much to say on this subject, but you might be interested in an answer I wrote to a related question.

Relevant section:

The general idea behind Soviet turizm was that Soviet citizens would travel to a particular place of cultural or historic note for edification and education, as well as camping and strenuous physical activity. One area in particular that tended to attract a lot of organized travel domestically in the USSR was the Baltic, especially Riga, Tallinn and the Latvian and Estonian coasts, were something of a domestic "Europe" Soviets could travel to and admire for their history, and architecture, although by the 1980s more tours were taken abroad than domestically. The Black Sea, especially Crimea, Sochi, Abkhazia and Georgia, were more destinations for sun and sand and for otdykh (rest) at spas (it's worth noting that Abkhazia in particular has a subtropical climate). Other forms of group tourism that were undertaken in the Soviet period were "scientific tourism" (ie, scientists and specialists traveling for specific purposes outside of international congresses), and "Youth Tourism" (especially for such mass international events as the World Festival of Youth and Students, which was held in Moscow in 1957 but in other locations before and after) and international exchanges.

It's worth noting that vacationing in both contexts was generally set up as group activities: namely, if you were staying in a sanitorium, or on a tour, you did it as part of a group. Soviet did of course get their vacationing in in more individualistic ways, but this was more "off the books", and probably would involve spending the weekend or holidays at a dacha (country house), which may or may not have been privately owned by a particular citizen or his/her family (the rules differed by time and place). Of course even spending time at a dacha had a productive aim as well, as a large amount of gardening was usually done there.

Just to give a sense of the figures: in 1980, out of a population of approximately 262 million, an estimated 188 million people took a holiday away from home. Of the 40 million Soviets taking vacations at organized vacation destinations, some 17.5 million were staying at spas or rest homes, and some 22.5 million staying at tourist bases.

Some 4.3 million Soviets traveled abroad in 1979. It's worth noting that most of this travel was to "friendly" (especially socialist) countries, but all international travel involved a process of being approved for an exit visa to authorize travel abroad. This involved applying for travel with one's Trade Union or Komsomol (Communist Youth) branch. Then a provincial party committee, usually with commissions of party, trade union, and KGB representatives, would review the application (with special attention on those traveling to capitalist countries). Once a Soviet citizen was accepted for travel abroad, a list of people assembled for a group, complete with character assessments, completed questionnaires, medical forms and a payment to Intourist's State Bank account, were forwarded to Intourist for processing. Those who were approved for travel often (if not always) had some sort of party connections (academics, factory managers, functionaries, etc.). State-provided vouchers would cover travel expenses, and an individual approved for travel was just that - an individual approved to join a group. You didn't take friends or families along.

The top 10 foreign destinations for Soviet travelers in 1980 were, in descending order, Bulgaria, East Germany, Czechoslovakia, Poland, Hungary, Yugoslavia, Finland, Romania, India and Cuba.

So, to summarize - if you were interested in international travel, you had to submit a request through either Komsomol or your Trade Union (ie, through your place of work). That application would be reviewed by local party structures, and if you were approved, there was still a lengthy vetting process before you were approved for an exit visa (this was a bigger obstacle than gaining an international passport) and added to a tour group. All travel and related logistics would be handled through Intourist.

Also, a side note on the OP premise - someone's grandfather who met British or American soldiers in Europe during World War II might talk a bit about it at home in the 1960s, but would probably be very reticent about such encounters, as especially in the Stalinist years such interactions with foreigners would be officially suspect and could lead to an investigation or worse.