In November 2005 my girlfriend and I went to see some of the Italian capital. We were most interested in the ancient part and The Vatican City.
We walked a lot around in the city, as all major tourist sights are within walking distance. Eventually we used the Metro, which works perfect and is cheap.
There is a lot of culture to see in the city, and the late autumn isn't such a bad choice of time, because it's fairly easy to get to see the different things without waiting for hours in queues.