Sounds like you can do 4 nights in each spot - which is a very nice amout of time. In Rome, I'd suggest staying around Largo Argentina,
Piazza Navona, Campo de'Fiori area, then you may walk everywhere. If you save a few euros staying by train station you will spend a lot of time on 42 and 64 buses going to and from centro storico. Christmas Eve is a mad house. A wonderful party in the...