Exactly as I always say when walking it's often what you encounter between the famous landmarks that is as interesting as the destination.

Thanks for the info on proximity! I'm looking on Google maps, but unless you're there it's hard to visualize.

Colosseum/Forum area is well south of historic center - Vatican is fair bit northwest or so but otherwise so much in a compact area - just love wandering around places like Piazza Navona and tiny lanes around Trevi fountain - really just do the other two sites on one day and roam the center on another. Maybe day trip to Ostia Antica - classic Pompeii-like ruins of Rome's ancient port a short metro ride out.