Neat idea for a course. This immediately brought to mind Baudelaire's idea of the
flaneur, which you might want to look into. When I was studying this, the book we read was Andrew Breton's surrealist novel
Nadja. It's not really my cup of tea, but it's about a man who falls in love with a woman he meets on a chance encounter in the street and he continues to walk the same path everyday on the off chance of meeting her again.
Other books that jumped to mind, but are pretty canonical:
Alice's Adventures in Wonderland
Gulliver's Travels
Dante's Divine Comedy (the ultimate spiritual journey!)
Chaucer's Canterbury Tales (in which each of the storytellers is on pilgrimage to Canterbury Cathedral to pay homage to Thomas a Becket)
Boccaccio's Decameron (which the Canterbury Tales is largely based on)
Lolita (there that long middle section in which Humbert Humbert and Lolita are driving across America)
And I would be remiss as a medievalist if I did not mention The Travels of Sir John Mandeville.
You might also want to consider literature in which characters are physically or spiritually lost, as a point of comparison.
Ah, here's one a non-canonical one that your students might enjoy. It's called
Winterdance by Gary Paulsen, and it's a nonfiction book about his experience running the Iditarod (a long and strenuous journey, physically, mentally, and psychologically) with 15 memorable dogs. The first section is a side-splittingly hilarious account of how Paulsen acquired the dogs and tried to train them. They did practice runs by having the dogs haul a broken down old car through the woods at night...I remember a particularly funny run-in with a skunk.
The rest of the book documents the alternate hilarity and horror of running the actual race, during which the author develops a tragic heart condition.