The Pantheon is quite close to Piazza Navona. You should plan a stop there.
If you go to St. Peter's try and hook up with one of the free tours. These are done by university students (tips allowed). It lasts about 45 minutes.
Try and eat at da Baffeto .It's on Governo Vecchia near Piazza navona and is very popular. Some consider it the best pizza in Rome.Get there when it opens at 6pm (this is very early for an Italian dinner). Another great pizza and other good food is at La Sagrestia at Via del Seminario, just besides the Pantheon.
I've eaten at L'Orso 80 many times for it's inexpensive antipasti,but lately it seems to be going down a bit in quality.