Etruscan ruins that can be reached by train

Orvieto has some Etruscan caves, a couple museums with Etruscan artifacts, in addition to some bits of a ruined castle (not Etruscan I think), with the benefit of being just an hour by train from Rome and a very cute hill town. Rome also has an abandoned city, Ostia Antica, nearby. There is also the Etruscan Museum in Rome that has Etruscan artifacts, not far from Villa Borghese. Another nearby town to check out is Tarquinia.

From Florence it is easy to get to many towns that were part of the Etruscan empire. Cortona, Volterra (by bus), and Chiusi.

Perugia is a transportation hub and has Etruscan ruins. The Villa Giulia is the National Etruscan Museum, in Roma. There is a train/bus combination that will get you from Roma San Pietro to Cerveteri in a little over an hour.

Volterra has an Etruscan gate and an extensive Etruscan museum (2 hours each way by bus from Florence). Cortona has remnants of an Etruscan wall and a small Etruscan museum (about 1.5. hours by train to Camucia-Cortona, then a short bus ride). Train from Rome to Orvieto is direct, 1.25 hours, and can also be visited en-route to/from Florence (bag storage available at the nearby Hotel Picchio, not in the train station).