I've been to Italy on three occasions, and I've done the Rome-Florence-Venice thing.
Here's my advice. Frankly, I think that Italy is going to lose a lot by December. The latest in the year I've been there was late November (Rome) which was actually very pleasant, because it was beautiful fall weather, 60ish, overcast, with the few decidious trees still having large golden leaves. Florence, in particular, is going to lose a lot in winter, or so I think. Florence and the valley its located in have breathtaking natural beauty in summer, and I can't imagine it will be the same in December. The good news though, is that Italy having lost a lot is still effing wonderful.
Do Venice, and do it at night, particularly if you're there with a sweetheart. I went there the first time during the day in July(miserable heat/crowds), and then I went back with my girlfriend last May and stayed in the city, which I hadn't done previously. It was downright magical. The ponte rialto, all the shops and winding streets, and *especially* piazza san marco at night were really breathtaking. There were quartets playing disney-esque music in St Marc's, and if I had a ring in my pocket, I probably would've proposed on the spot. Its really special. The lights in the city and the ambience at night are great. Someone said something about it being dead at night. Thats why I liked it better, because it wasn't crowded. Weather will be an issue, though. It rained a bit when we were there, but we still had a great time. The train ride on the eurostar isn't bad, and it only costs 35 euros. A helluva lot cheaper than deutsche bahn. Also, the shops that sell murano glass/carneval regalia are really fun to browse, and even more so at night.
As for florence, I would say do it, and give it two to three days. The food is wonderful, and its a nice and neat town. However, you need to know where everything is. I know Rome like the back of my hand. However, when I was in florence in may it wasn't as good as when I had been there before with my uncle, who knew where all the cool and fun stuff was. Still, the S Lorenzo street markets, the loggia dei lanzi, the ufizi, and the bridges and piti palace/other stuff on the other side of the river Arno are well worth going there. I've heard Piza is way overrated. Another option, I think, is Asissi. Its a really nice place and the food is good. Worth a day if you could find some cool place to stay there, like a country guest-house or something. Its a very small town. I think its about an hour away from Florence by highway, but I may be wrong.
You're right on focusing on Rome. Its really my favorite city in the world. I hope to be able to live there one day. There's nothing quite like a saturday night going out to dinner with your lady friend in the neighborhood of the Pantheon (be careful about picking a restaurant - many tourist traps). There's so much to see and do in Rome. I'll be happy to provide particulars if you wish, but a lot of what I do there is academic and not sartorial. I haven't had the money to do shopping there in the past, but I did buy a very nice tie on sale at a shop the name of which I forget...