The underground parts of the Colosseum require special tickets for entry so make sure you get those ahead of time if you want to see those.

In the nearby Forum, look for the Temple of Caesar which is where Caesar's body was cremated and don't miss the Palatine Hill Viewpoint overlooking the Forum.

Across town, don't miss the Pantheon, the nearby Curia of Pompey where Caesar was assassinated, and the statue of Giordano Bruno.