Hi Veru9,
3 days is so little time that just exploring by walking could take a lot of time. I was there last summer with my 9, 12, and 14 year old's for 5 days. The Coliseum was a hit. We also did a Vatican tour so that we could get in without waiting in lines. We spent one day going to the Borghese museum (wait) and then exploring the park it sits in. The kids and hubby rented - what are they called; those stand-up scooter things. We had a picnic and walked around. And then we walked from there back to our base-neighborhood (Trastevere), passing the Spanish steps, Trevi fountain, Piazza Navona, the Pantheon, and Campo de Fiori - even though we had already visited the Pantheon on another day - but that walked gave us a great sense of orientation in Rome. Walking around the Trastevere neighborhood was another pleasure, especially in the evenings. The day we visited the Vatican (we started the tour at 7:30a, so were done mid-morning), we walked from there to the Pantheon. The day we visited the Coliseum, we walked from the Trastevere neighborhood there (30 min). You get the idea. By the time we left, we'd visited sites but also just immersed ourselves in the central city and felt like we knew our way around and had a feel for the place.
You could take a day trip to Ostia Antica. We considered this, but in the end, it took those 5 days to feel sated on Rome.
Finally, I'll make a plug for the Capitoline museum. This was an add-on (we hadn't planned to visit ahead of being there), and it was stunning. Its mostly artifacts and sculpture, as opposed to artwork, which tell a story of the history of Rome. It brought everything we were seeing into relief. (The Borghese museum was also stunning but much more artsy)
And while not all the kids wanted to do all the activities (meaning, my 12yo son!), he really appreciated it after we were home (despite complaining much of the time while there)...
hope that helps,
Jessica