The train station is very close to town as the bird flies, but it is a winding hilly road so it is a bit of a climb. Castelgandolfo is a very small and quiet town, no tours of the papal residence that I am aware of.
Public transport is pretty bad around there, but there is a place to eat that is wonderful, very spartan but lakeside and with wonderful porchetta, mozzarella, bread, olives etc. It's called Da Agnese. Would be a short cab ride from the center to get there (it is also cheap to rent bicycles and several places on the lake provide them).