What to visit in Rome?

I'm going to Rome this summer because I started taking Latin this past year and looove it. I've been once before when I was way younger and I didn't have such an interest in the actual historical sights, but not I am determined to learn a looootttt. So what are some of the best things to visit? Not only as a tourist, are there any other Latin students out there who can direct me to the most fascinating sights?