We really enjoyed the Capitoline Museum. You'd better have a working knowledge of Roman art and/or a good guidebook, because everything is jumbled together and not always well-labeled -- kind of like your grandmother's attic, if your grandmother had a bunch of Roman antiquities!
The Keats-Shelley House at the foot of the Spanish Steps is well worth a visit if you're fond of the English Romantics. It is a rather eccentric British-style small museum with an amazing library, paintings, Keats' death mask, and many other interesting things!
Pompey's Theatre (where Caesar was assassinated) is well below modern street level, in a block where they were supposed to build an office building, but didn't because they found the theatre. It is also a cat sanctuary - we were up on the modern sidewalk and a big ginger tom had us sussed for patsies . . . scaled the wall and spoke to us for awhile. Sadly, we had no treats.
wow, great tip!