I have added photos of our trip to Rome in early November. It's fast becoming one of my favourite things to do, this going to a European city in November for a week. I had loads of things I wanted to say about Rome, but there's just too much of it. So, let me recommend a few things very briefly.
First, we stayed here. The lady who owns the apartment is a very friendly American lady, and the apartment is where she actually used to live, so it's got a proper "someone lives here" feel about it, rather than the more usual "it's too small to actually live in, so I'll rent it out to tourists" feel that you usually get. That said, it really only sleeps two people. However, the location is fantastic. We walked everywhere from here; the only time we got the bus was when we were going to the Villa Borghese. We also ate in a bunch of places that our apartment lady recommended, and they were all very good.
My favourite places to eat and drink were here, which does amazing fried artichokes with salt and pepper; here, where we ate fantastic pizza on a Saturday afternoon and watched trendy Roman people go about their well-dressed Saturday; La Scala, which is in Trastevere as well and does the most amazing orange risotto; and this cafe, which does the strangest sour/sticky sweet coffee you ever tasted, in a beautiful 1950s bar.
We also availed ourselves of a private three-hour walking tour, which can be booked by talking to the lady who runs the apartment and brought us to the Forum by a route we never would have thought of by ourselves and which helped us to make a lot more sense of the layout of the ancient city than we would have got by other means. So I would recommend that too, if you've much of an interest in the ancient times.
(I also really liked the dog park in the Villa Borghese, and the cat sanctuary among the temples in the Largo Argentino.)
It is exhausting, though, and really, really crowded. There are people everywhere, all the time, and there are always mopeds up your arse and cars trying to squeeze past you on the narrow streets, and there are no footpaths and everything's cobbled, which sounds lovely but means you have to watch your step. So if you're going, you need to build in some rest time during the day.