I will be spending a week in Lucca this summer. Any suggestions for easy day trip destinations? What can I reach via train? Any advantages to renting a car for a couple of days?

I would definitely rent a car and drive up the Sercchio River in the direction of Barga. See Barga, Castelvecchio Pascoli (the poet's birthplace) and Castelnuovo and into the Garfagnana. This is an area between the Alps and the Appenines, quite hilly and like a national forest. Very pretty scenery with tiny little towns. Not much English spoken, not many American tourists.

to the top

Try Montecatini Terme. Totally different than most of Italy that I have seen. Almost tropical like with palm trees, parks, flowers. This is the spa area and a nice place to relax. Take the funicular to the top. Great view. Close to Lucca by train.

The Cinque Terre is an easy day trip from Lucca. Lunch overlooking the Med and maybe a hike or boat ride between the small towns. Beautiful views.

Don't forget the obvious---you'll be in the Toscana region of Italy. So take your rent car & drive around to many of the lovely small towns in that area. OR, if you want to go for larger city, Florence is a quick & easy train ride from Lucca.