I love, love, LOVE to travel because experiencing new places enhances my two other favorite things: reading and writing.
I usually try to read something related to my destination. My daughter is heading into her senior year, so all of our recent travel has involved a small liberal arts college - or four. Last fall a trip to Minnesota prompted me to read Sinclair Lewis' Main Street, a delightful novel that brought texture and history to the small towns we visited. I also made a point to read more F. Scott Fitzgerald, making the drive past his old house in St. Paul a particular thrill. I also try to bring home a few books with local flavor to read later - and that's when the real delight of travel comes. I love being able to really picture a city that I have experienced myself. I think it also helps my writing to see how other writers use location in their storytelling.
Sometimes I work on fiction while I travel. Part of the search for a great college fit has involved finding the cutest coffee shop in town. If only the love for a cute coffee shop always correlated with the love for the college! I've enjoyed adding to my WIP while my daughter keeps up on homework. Most of the time when I travel, I leave my WIP simmering, and limit my writing to my daily diary entry. I can't pretend that these are polished words - but it's always enough to spark the richer memory of some detail I might otherwise forget. Most trips - even to a liberal arts college in the middle of Ohio - lead me to some sort of story idea or potential character. That's the best part of travel - so many new experiences, so many new ideas.
I feel certain that any corner of the world, seen for the first time, will inspire a writer.