Restaurant: The Little Orange - Al Piccolo Arancio which is in an alley close to the Trevi Fountain. Highlights are the fried squash blossoms, the fried artichokes and the ravioli in an orange cream sauce (not what I would usually order but WOW!). I will tell you that I sent cousins of my from Miami there on their trip to Rome - the ate there the first day and never went to another restaurant after!
Gelatto - people will tell you this place is the best, that place is the best. I am telling you - there is none better in Rome than Il Gelatto San Crispino which is also close to the Trevi Fountain.
Both places have websites which are easy to find online. I did not post them purely because I was not sure if it would be breaking any forum rules.