If wine and fine dining are your interests, I'd head to Sienna and the wine country where there's great scenery and possibly even greater wine. You may want to rent a car to get there though so you can stop and "smell the roses" along the way.

You can also just stay around Naples and visit Sorrento instead of going on further to Pompeii. Although not really known to be the friendliest place, Naples is a really good city to explore on foot. Sorrento, on the other hand, is a good place to do all the touristy stuff and you can visit the Amalfi Coast and the island of Capri. It's a beautiful place!

Last year when I was in Rome during Thanksgiving, I got very lucky and the weather was still warm and the skies clear. It was good to head to the beach to escape city life though and take advantage of the good weather.

I second Florence. If you plan to stay there overnight, I'd recommend staying a place where you can have a view of the Ponte Veccio.

Florence is just two hours away from Rome if you take the train. It's a gorgeous city that exudes history and architecture. Just look at all the great cathedrals there! Wonderful art museums as well.

Unless you're flying, I would say that Venice is out of the running so another good trip to make is to Pompeii to visit the archeological site, which is about 2.5 hours from Rome. You can take the morning train from Rome to Naples, transferring to Pompeii. I believe the earliest train leaves at 6:45am, but you should double check that. You can either book a tour and guide beforehand or arrange it there. Or if you're seeking some alone time, you can purchase an audioguide and get maps from Information. Also, if you book the tour beforehand, you can also get a guided tour of Naples also! Herculaneum, nearby, is also a great place to see architectural ruins.