Perhaps not 'well-travelled' but more the 'furthest travelled' but in the early second century, Ptolemy records in his Geography that a contemporary of his, Maes Titianus, travelled as far as the Himalayan foothills. A merchant who was looking to secure a direct supply of silk from China, known to the Romans as 'Seres', Maes stopped at the 'Stone Tower', a famous milestone on the Silk Road which was situated in what is now called Tashkurgan, in far-western China.
I'm not sure if you consider him from antiquity but Ibn Battuta was a Moroccan explorer in the 14th century who, over thirty years, traveled across most of the known Islamic world and other non-Muslim places. He made it around to several parts of Africa including the north, the west, the Horn of Africa; he even journeyed to Central Asia, China, and Southeast Asia.
If we are talking people who documented their travels:
Marco Polo would be a pretty good candidate. He travelled from Venice to China and back with his uncles, who had already done the trip once. See his book Livres des Merveilles du Monde or the countless translations and adaptations.
In ancient times Herodotus would be a good example. He travelled widely across the Mediterranean and documented it in his Histories.
Nobody has mentioned Ibn Khaldun, if I have the name right recalling history lessons from two years ago. He was originally from Africa, I belive, but made the Hajj something like seven times, went to India, Europe, and everywhere in between.
Then Zheng He, captain of china's fleet, which - although not with their captain - traveled to Mesoamerica and the middle of the Atlantic, and probably discovered Magellan's famous passage a hundred years prior to his voyage.
Of course they're not western, so western schools neglect them.