Gosh, where to start. Campo dei Fiori is lovely, and also the area that was once the Jewish ghetto. Trastevere over on the other side of the river is also very nice. As for what to see, all the usual sights - Roman forum, the Pantheon (my fave), trevi fountain, spanish steps, vatican city and st peters etc. As for eating - for lunch anywhere with basic decor, no menus and lots of old local folk eating there is a good bet! Spaghetti alla carbonara is a Roman dish, and also puntarelle which are a kind of chicory that as far as I know you only find in Rome. There is a great restaurant in the Jewish ghetto called Da Giggetto that is very lively in the evenings and delicous food. There is also an amazing gelateria near the trevi fountain that only offers flavours made with fresh ingredients that are in season - I think it's called San Crispino. I'll never forget the pear sorbet I had there... Edited to add the name of the salady chicory things that I couldn't remember at first, and also the amazing gelateria