If you have time, walk up through the rose gardens to the Piazza of the Knights of Malta - peer through the keyhole in the gate there, for a lovely view .
The Pantheon was my favourite place, really beautiful, but I second just popping in to any church you pass, they are stunning (even my DH enjoyed them, and he usually isn't bothered by that kind of thing)
If you like wine, visit Cul de Sac, just off the Piazza Navona. It's pretty shabby (Formica tables), but the wine list is amazing - ask for the full list - with all the bottles on shelves above your head. Pretty decent meat and cheeses to accompany.
Trastavere is so pretty in the evening, just wander the streets stopping at whatever restaurant takes your fancy. There are also several bars doing aperetivo - usually a free buffet for the price of a drink. Makes a great starter, or small meal.