Go for the history
You know why you want to go to Rome. It's full of rich history and amazing sights. The metro is easy to figure out, or go rent a bike or something. The food is all over the place and delicious. Find somewhere and grab a liter of wine with some friends.
Insider Tip:If you're an american, remember that most shops close between lunch and dinner. Dinners start later than most americans eat dinner as well, so plan ahead. Also, don't get the ROMA pass! It's convenient, but it's not that great of a deal. Don't forget that the Vatican City is not Rome, so the Roma pass wont work anywhere there.