Trains travel throughout the length of Italy. Some larger cities include Milan, Brescia, Padua, Verona, Genoa, Trieste, and Rome; in southern Italy Palermo, Reggio di Calabria, Naples, Brindisi and more
Traveling first class on the Eurail---private cabin with own bed, built-in alarm clock, two blankets and a comfortable pillow, bottles of water, and soap in the private bathroom with shower. There was space for luggage under the bed. Extremely do-able!