I always thought it's a kind of a prerequisite for being a monk or at least a part of their job to travel the world
In England I think most monks lived in Monasteries centred around an abbey, and would never travel more than a few miles away.
If you have access to any Brother Cadfael books, TV episodes, or books on tape, you can learn a bit about Monks in the 1140s, and things didn't really change until the Reformation (when Henry VIII confiscated most of their lands and destroyed or took possession of the abbeys). Cafael is a detective, using his knowledge of herbs, healing, and the study of human nature to puzzle out his cases.
Brother Cadfael is unusual in that he frequently travels away from the abbey, but always with the permission of his Abbot for a specific purpose. Of the other monks in his monastery, only a few travel at all.
I'm not an expert on medieval monks mind you - there were many sorts (Dominican, Augustinian and Franciscan to name three), and maybe some travelled more than others.
Yet another subject I need to learn more about, sparekd by my Playmobil hobby!