Three days isn't long, but I would do the following:
Day 1: Vatican & Vatican museum (possible to do both in one day, but don't hang around!)
Day 2: Colosseum & Forum (Colosseum isn't actually that exciting, the Forum is incredible though)
Day 3: Trevi Fountain (10 mins literally), Spanish Steps (again 10 mins), Pantheon, and then whatever else you fancy doing. Shops are nice, and I'd just take a break in the Piazza Navona for some grub. Relax, soak it up. If you really want to see more stuff though, go to the Castel Sant Angelo: It's huge!
Also, while you're by the Spanish Steps go and have a look inside the Shelley/Keats museum. Sounds silly to do when you're there, but we found it to be one of the most interesting an curious things in the whole city. Probably take about an hour to do it all, but fascinating if you have any interest in English literature at all.