Christmas time in Italy

Assuming your travel days to and from Italy don't include the 21st and the 28th, that gives you 8 days on the ground. Since Christmas falls right in the middle, I would personally limit myself to 2 cities. However, you could structure your trip something like this: Rome: 21st - 23rd Florence: 23rd - 26th (spend Christmas in Florence) Venice: 26th - 28th. As to hotels and restaurants - that's a pretty broad category - high end, middle, budget??? Some restaurants will be open Christmas day - as to which ones that really depends upon where you are staying since public transportation on Christmas is extremely limited to non existent. Your best bet is to decide upon your hotel and then ask for recommendations here. Also, the hotel can be very helpful in this regard - especially for Christmas Eve when the restaurants are busy!!!
As to sights, same observation - what is a "must see" to some is "overrated" to others. Best bet is to get some guidebooks and have everyone look through them and list what they most wish to see in the cities you decide to visit. As to making train travel easier: Pack light! Train travel in Italy isn't complicated and works pretty much like it does everywhere else in Europe. For travel between say Rome and Florence, only advantage to buying tickets in advance is price - since it will be the holidays, if there is a particular departure time you want, buying in advance guarantees a spot on that train - normally this isn't an issue, but during the holidays the trains are busier.

I concur with Nancy: stick with two cities maximum. I have previously posted about Christmas travel in Italy, particularly Rome here. Rome is spectacular and there are actually things open on the 24th-26th, but you have to be flexible, search and plan a bit.

I haven't done Christmas in Italy but I would end in Rome. If you can bear crowds I would try to get to christmas eve mass in the vatican.