• Ibn Battuta should be your first stop! The Hakluyt Foundation publishes the most comprehensive translation I know of.

• In Medieval West Africa: Views from Arab Scholars and Merchants, Levtzion and Spaulding translate the "interesting parts" of various Near East Arabic writing on West Africa, either firsthand travels or secondhand reporting. (I also own the unabridged translations, Corpus of Early Arabic Sources for West African History, hence referring to the former as the "interesting parts.")

• The Travels of John de Mandeville is now understood to be a pastiche of sorts and fantastical, but it was enormously popular reading in the Middle Ages and early modern era.

• The Pilgrimage of Egeria is one of our earliest writings definitely by a Christian woman. Egeria, who probably came from Roman Spain, kept a record of her journey/pilgrimage to various holy sites in the Near East.

Those are some fun ones to get you started. :)

I'd second the recommendations of /u/sunagainstgold: Egeria is a lot of fun, even though we're missing much of the text. And a handy collection of travelers and geographers like Ibn Fadlan may be found in Penguin's excellent Ibn Fadlan and the Land of Darkness.

Missionary accounts can also be a lot of fun. I'd point you to Ian Wood's The Missionary Life, which is perhaps the best introduction to a large number of them. One of my favorite bits is when the Archbishop of Hamburg starts worrying that after he converts Scandinavia, he'll probably encounter the dog-headed people rumored to live on the edge of the world and he starts taking a straw pull of other churchmen to see if he should preach to the dog-heads as well. (The letter that survives is in Dutton's Carolingian Civilization: A Reader.)

And perhaps my favorite medieval text of all is the Cosmography of Aethicus Ister. I'm pretty sure it's the Finnegan's Wake of the late Merovingian world. The author claims that he is Jerome, the guy who translated the Bible into Latin around the year 400, and he says that he found an old geography book by a certain Greek philosopher supposedly named Aethicus Ister, and so he's decided to summarize it and adapt it for Christian audiences. Of course, this is all fiction. There's clear references to events in the early 700s, and the Latin is really, really bad, and sometimes intentionally punny. Obviously not the work of 'Jerome', and it's doubtful that 'Aethicus Ister' ever existed. This geography textbook is actually a work of fiction, surveying the peoples of the world to both entertain and to comment upon contemporary events. The edition linked above has a very thorough introduction and a full translation into English, which is the first translation of this really weird text into a modern language. The editor, Herren, thinks that the author probably grew up on the Greek side of the Adriatic but was forced out during a war early in his life; he was educated in Western Europe, probably France but apparently spending time in Ireland and England, before settling down at Bobbio in northern Italy where he put the finishing touches on his text, which soon found an enthusiastic audience in Bavaria. It's a romp.

Wood and Aethicus Ister are, admittedly, rather expensive at most places where I can find them, so if you're interested, you might want to borrow them from your library. Aethicus Ister might strike you a lot like Mandeville, but I think that Herren's introduction does a brilliant job showing how this isn't just fantasy.

And of course there's the Vinland Sagas. If you're interested in how anchored these are in reality, reference Birgitta Linderoth Wallace, "L’Anse aux Meadows and Vinland: An Abandoned Experiment," in James Barrett, ed., Contact, Continuity, and Collapse (2003), pp. 207-238.