After You've Done St Peter's And The Colosseum...

Galleria Borghese
After grabbing a cappuccino and a cornetto, head to this gallery for some beautiful architecture and sculpture from the Baroque masters.
San Carlo alle Quattro Fontane
An almost musical Borromini church tucked into this little corner off the beaten path. Check out the view down the Via Delle Quattro Fontane!
Fontana del Tritone e Fontana delle Api
Not as hyped as the Trevi fountain, this Bernini fountain has a much more rustic feel. Grab a panino at any nearby shop and an Aerol Spritz, a local drink that can cool you off on any day of the year.
Jewish Ghetto
Spend your afternoon strolling through the Jewish Ghetto. Don't bother with the museum, but make sure to stop into every book/fabric store and synagogue for a real taste of life here.
Orange park
Make sure to grab a peroni and head up to one of the hills for sunset - my favorite is Orange Park, and it's less well known so you can scope out a seat right on the ballaster and get an uninterrupted view. Spectacular
After You've Done St Peter's And The Colosseum...
St Peter's keyhole
Before you leave the hill walk down a block to the right and you may see people crowded around the entrance to the Sovereign Military Order of Malta. Why? If you look through the keyhole you get a perfectly framed St. Peter's. Keeper of the keys!
L'asino d'oro
One of the most fabulous restaurants in Rome and not too expensive, make sure to eat a proper Roman meal of many courses (definitely try to the linguini with liver pate), and if you get there before the Romans (8 o'clock) you won't have too hard a time getting a table.
Ai tre scalini
This fun neighborhood is always guaranteed to be full on any day of the week, and has a great local vibe, though the bartender's speak english and the locals are more than willing to try their slurred English on you. Also probably one of the few places in town where you can grab a proper beer.
If you're still up, head to Trastavere, a nearby neighborhood with good bars and dancing. Avoid the bars with drink specials as most of those are filled with tourists and international students (unless that's what you want), and try to find one with the doors closed - that means they're not necessarily looking to be flooded with out of towners.