People in certain professions may have traveled much more than others, and they would likely have a different point of view, but there are times (such as wars) when large groups of people were given cause to travel considerable distances. Do we have much information on what someone would consider to be "far away"? If you told someone they would have to travel to a neighboring region, would they consider it a great distance? What about across France? What about from Italy to the Holy Land to crusade?
You hear a lot in history about armies and what have you traveling these distances, but never any mention of the fact that these armies are often traveling kind of a long way, especially for the time!
I am equally interested in other places and times, but I thought it better to define the question more specifically.
This is a really interesting question that you can get a lot out of by looking at two big factors: which people groups were most mobile, and what routes had major thoroughfares through them. I can't speak for armies, though.
The first you can kind of think through economically: if you're a European peasant bound to a certain plot of land and have very little money, chances are you don't have any reason or incentive to move, and they usually didn't start moving until post-Plague economics changed things. On the other hand, if you're a merchant, traveling is your life. But one group does have an interesting mix of poor and rich that give an interesting picture of mobility: the Ashkenazi and Mizrahi Jewish population. Barred from holding land, medieval Jews were necessarily disposed to more mobile careers, and they kept up a scholarly and mercantile elite that traveled often...at least, the men did. Jewish women's perspectives give us great insight into the different perspectives. In Ashkenaz (Franco-German Europe), Jewish law prohibited husbands from forcing their brides to move to another city outside their native country, but they could take them to any city within the country, even by force (where 'country' is defined by the dominant language). Even so, European Jewish women most often married close family--first cousins or uncles were ideal, because it let them stay at home in the tight-knit communities they knew well. European travel was also very dangerous for Jewish women; in a letter about safe travel practices for women, one rabbi complimented the idea of dressing up as Christian nuns to get by safely. Betrothals to promising scholars or merchants from neighboring countries happened, but they were uncommon, and there's one case of a woman's father fighting to break her betrothal for over 10 years when the distant groom became ill and his prospects dropped. Things were a little different in the Muslim world. Most of our information on them comes from Egyptian ketubahs, marriage contracts. It was more common for women to be married to business partners and academics far away, which often leads to clauses in contracts allowing the bride to visit home regularly, for fear of their daughters going to foreign households to demanding in-laws and unsympathetic older husbands. It was also common for Jewish men to travel long distances for business or scholarly networking, so much so that they sometimes started second families in other cities, or just abandoned their brides altogether, which is why several ketubahs sport divorce clauses letting the wife divorce the husband if he doesn't show up within 18 months (European law required he send financial support every 6 months), to give you an idea of what constituted a "long time away." Older Jewish women, on the other hand, were often widowed, not tied to anything but her business, and often had enough money to travel, so they were considered "travelers par excellence," and would bounce between groups of an extended family between cities, carrying letters and news and generally keeping everyone together.
What all that implies is that distance was relevant to your community and how far you could go while still staying in touch. Christian villeins rarely went far from their villages, and Jewish daughters were reluctant to go far unless they had to, because those were their home-ties. Getting cut off from the people you grow up with and depend on is a much bigger deal in a society where you either can't read or can't afford many letters, and if you weren't a merchant, it took an awfully lot to up and move--if you're bound to your land or your household, you've gotta think about who'll take care of all that while you're gone. One letter from a Jewish merchant shipwrecked in Sicily to his wife in Cairo said that he'd like her to come settle there with him and pay for it, but he'd understand if it was too much and offered to agree to a divorce. The distance obviously wasn't phenomenal for a trader, but moving a medieval household is another thing entirely. Even literary sources give us a hint at what distance meant: the Tristan and Isolde story features an Irish princess getting sent to Cornwall to marry, and it's such a long distance and such a risk that Isolde's mother gives her a love potion to make the king treat her well. Of course, that doesn't go according to plan, but you get the idea--there was a lot of anxiety about home-bound people moving.
As far as routes, it's useful to think about what places were major hubs in the medieval world and how busy those roads might be. Rome? People came and went constantly, especially religious types. Same with Paris, Cairo, Florence, etc. Trade dictated what roads were busy and safe. Meanwhile, villages or other settlements that were more out of the way were naturally less-traveled, and 'the unknown' is a powerful barrier. Which is why England to Italy might not be a terrible stretch, but delving somewhere without a major trade hub at the end of the road would be a huge risk with little to show for it.
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I'm not sure that this question can ever really be answered the way it's phrased, since if something is 'far away' depends hugely on the context. For example, anything more than 5 minutes walk is 'far away' for me if I just want to pick up some bread and milk, but going to Spain isn't far away for my summer holidays, while going to China is. There's a great document from England from right at the end of the 12th century, where a man is told to go on pilgrimage to Jerusalem as penance for adulterous incest. When he complains that it's too far and he can't afford it, the local abbot judging the case sends him to Rome to have the suitability of the penance judge by Pope Innocent III. Does this mean that Rome wasn't far away for a 12th century Englishman but Jerusalem was? I don't really think so - it all depends on the context.