Vagabond19,
I also agree that's a pretty short trip to cram Rome, Naples/Pompei, Venice and possible Florence into. Remember, just because train travel between Rome-Florence-Venice is between 1.5 and 2.5 hours (frecci or fast train), you still burn time packing, checking out, navigating to the train station, navigating to a new hotel or apartment, checking in, unpacking, etc. The better part of the day is shot by changing cities unless a lot of care and attention to detail is used.
The Italian cities you mentioned are in essence gigantic museums. So, I'm a little curious what exactly you want to see and what you are expecting given that you say you aren't "much into museums."
One week in each of the cities listed is about the right amount of time to get to know, at a very basic and simplistic level, that one city. It gives enough time, especially considering short days and short attraction hours of the late autumn/early winter, plus time to do a day trip or two outside the city.
Additionally, given the late autumn/early winter time of year, the weather becomes progressively unsettled the further north, and closer to the Alps foothills you get.
I would recommend sticking to just Rome and doing a day trip or two to the surrounding countryside and/or Naples/Pompei. You could even do a day trip to Florence as it's only a 1.5 hour train ride and most of the major tourist sites are a 10-15 minute walk from the train station.
Staying in Rome the entire time also affords you the opportunity to rent a holiday apartment which would be much more comfortable than a hotel room.