Italy Over Christmas/New Years

It will be much like it is in the US. Most shops and restaurants will be closed. If there were any restaurants open they are usually ethnic in nature as they don't typically celebrate Christmas either. The other option would be to get a hotel or apartment with a kitchen and then do a little shopping before hand. All three cities are big cities with more options for things to be open. However, I would try to spend Christmas in either Rome or Florence rather than Venice. Transportation will probably be a little better. I hope this helps some.

Sorry, Abe, I have to disagree. We've spent 3 Christmases in Rome (two as residents and one as tourists) and we have found plenty of restaurants open. It is best to make reservations, though, both the 24th and 25th. New Years Eve is a big dining out night with many fancy fixed-price dinners. Be sure to make a reservation. Katie Parla usually does a post on her blog telling what is open in Rome for the holidays, but many many trattorias are open too. It seems Italians like to dine out to on holidays too. I agree that Christmas in Rome is best. While everything shuts down on the 25th, you can still enjoy a nice walk and see a lot of sites/ruins, etc., and on the 26th many places reopen.

There are lots of restaurants open on Christmas day in Florence as well. Never spent the holidays in Venice, but it's probably likewise there.

Many (if not all) museums will be closed in all of the above cities, but churches will be open and some will have concerts.
Stores will be closed but people will come out in droves in the afternoon, after the huge Xmas luncheon, for a "digestive" window shopping passeggiata. Caffe' Bars will be open (at least many in the historical center).

New Year's Eve is like any day, so everything is open, but you need reservations at restaurants if you want to stay for the "Cenone" (Midnight Dinner) and prices for the Cenone are high.

New Year's Day is similar to Christmas day in that most places (museums, stores) are closed.