To understand Soviet economy, it's useful to flip your assumptions. The usual mindset is: "opening a business is a natural thing to do unless there's something in the way". In Soviet Russia, it's rather "any market activity is a crime unless explicitly permitted". That applied even to such basic occupations as merchants, let alone restaurant owners. Moreover, there wasn't such thing as a "market niche". If the ministry of food industry didn't open a Mexican restaurant in your town, there wouldn't be one; if it did, chances are you'd have to be a part of a certain group to visit it. For instance, there were diners for the members of the Writers Union which would have better cuisine than a regular diner that anyone could visit; if you were a diplomat, you would have access to even better food (as well as other items), etc. There's a good source on food history in the USSR but it's in Russian (still worth a try - Google Translate manages Russian quite well these days).

Luckily for you, there were at least two periods in the Soviet history when some laws were reverted. The first of them was from 1921 to ~1929. In 1921, the "new economic policy" was declared, which allowed, among other things, small business ventures. (For a more detailed overview, Allan Ball's book describes NEP in great detail.) You could open a restaurant and even hire a few people; soon enough multiple cities opened "Societies of Mutual Credit". A good way to start a business would probably be to become a member of such a society and get your loan. Furthermore, you could even ask a state-owned bank for a loan! Congratulations - now you're a "NEPman"! Your business is allowed to interact with other citizens as well as with state-owned syndicates under the watchful eye of the Commitee on the Matters of Private Capital.

However this wouldn't last for long. NEPmen were viewed as "small bourgeoisie", so, naturally, before long a media campaign against them began, and soon criminal charges followed. Perhaps one of the most chilling reads from that era is this (Russian) "research paper", written by a member of the Soviet government. It analyses the sources of the NEPmen's capital, but describes it as criminal by its very nature, categorizing it into "malicious dealings with the state structures", "predatorial rent" etc, and lists quite a few examples of businesses... suddenly ending one of them with "[this person] has been executed by now". (granted, that particular case involved a huge bribe).

But let's say you managed to close your restaurant, avoid the attention of the state and live peacefully until the 1980s (wow, you must be old!) Now you're in luck again - Gorbachov has declared the Perestroika. Since 1986, private self-employment is legal (tutors, taxi drivers...) Since 1987, you're able to open a "cooperative" which is basically a small business enterprise with some limitations. For one, you were free to produce goods by yourself, but officially you couldn't employ anyone. Since 1988, you could also participate in trading and basically all other market activities - so that's when you'd probably open your Mexican restaurant. Heck, they've even opened a McDonalds in 1990! (yep, that's a line. It's the first time ever all these people see a fast food restaurnt).

However, as you can see by the dates, it was already a countdown until the fall of the USSR itself - the anarchy that ensued is beyond the scope here.

I’m a Yugoslav specialist but my minor field was in Soviet studies so I’m gonna take a stab at this. My knowledge is best when it comes to the 1920s-1950s so my answer gets a lot more impressionistic towards the end. But hopefully it will still meet the mod standards and get the conversation going!

First off, it depends on what era you’re talking about. Early Lenin-era planning was a blend of massive 5-year planning and agricultural collectivization (which granted zero space for any sort of entrepreneurship like you’re talking about) and small scale market-based economics in the rural countryside. Basically, Lenin recognized the need to let small scale market mechanisms play out in the rural countryside since a) the peasants were not fans of collectivization; b) they didn’t have enough goods to trade for it to be a threat, i.e. the development of a rural “bourgeoisie” (literally, they were just too poor); and c) the Soviet authorities early on lacked the infrastructure to really control the massive size of greater Russia, and if they were to have cracked down in these sort of market mechanisms, rural society literally would have collapsed.

Fast forward to Stalin’s 20s and 30s and things change a bit, and to your question, would have made it all but impossible to introduce a new “niche-based” business. During this period, agricultural collectivization was ramped up like crazy and all the rural market-mechanisms I referred to before were essentially suppressed (although a decent sized black market continued in both the countryside and the cities). Meanwhile, urban centers were undergoing a state-led transformation based on the Western department store model. This may sound a bit crazy but it makes sense. Basically, the Soviets looked to Western (mostly US) models to modernize their consumer economy by developing large urban department stores ala Gimbel’s or Macy’s. This was somewhat a ploy to demonstrate to the world that communism could produce the same level of wealth as capitalism, and it rarely worked in practice. The stores were well stocked for media appearances and foreign visits but then otherwise were usually sparsely stocked. The goods themselves were also all state produced, meaning they were driven by Stalin and his bureaucrat’s ideas about what consumers wanted and needed. Surprise surprise, they were way off the mark! So, anyway, during this time (20s-30s) there would have been zero room for any sort of entrepreneurial endeavors.

For the rest of Stalin’s reign, things wouldn’t have changed much in regard to your question since the war dominated life in the 40s, and the late 40s and early 50s until his death were mostly geared towards reconstruction from the devastation of war.

From here, the question becomes a lot more complicated, and to be perfectly honest, I really can’t answer it. There were a series of economic reforms after Stalin’s death but they ultimately didn’t change much in terms of the state-driven approach to the economy, meaning I doubt there would be room for an entrepreneurial enterprise. Consumer needs were taken much more seriously from the late-1950s on but were still based upon central planning and not individual’s business enterprises.

That being said, when we think of the small scale level of local restaurants, cafes, tailors, cobblers, etc. it’s really unclear to me how it functioned. I’m assuming not everything was directly tied to giant state mechanisms but I’m really not sure how one would go about opening a new restaurant, for instance. My guess would be a rigorous bureaucratic process that entailed a good amount of nepotism and behind the scenes string pulling to actually get it done. But again, at this point I’m just speculating based upon broader trends.

Sources:

Randall, The Soviet Dream World of Retail Trade and Consumption in the 1930s

Healer, A Social History of Soviet Trade

Davies, Harrison, and Wheatcroft, The Economic Transformation of the Soviet Union

Lewis, Moshe, and Elliot, The Soviet Century

Zubkova, Russia After the War