Visit Rome with Kids
You'll never run out of things to do with kids in Rome! The Roman Forum is a good place to start - plenty of room to climb and run. At the end of the Forum is the Colosseum, where gladiators killed lions, and if you have enough energy, afterwards you can climb the Palatine Hill to visit the palace of the Roman Emperors there.
Your kids will also love the Golden House of Nero, because it's mostly underground now and creepy, like cave exploring (if it's open - it is often closed and sometimes you have to get tickets ahead of time. Ask at your hotel.) Nearby, you can walk to the Forum of Augustus, the Forum of Caesar, and then the Forum of Trajan. Up above the Forum of Trajan, and easy to miss, is Trajan's Market - the kids will be astounded at the resemblance to a modern mall.
On the other side of town, don't miss the huge round temple of the Pantheon, or St. Peter's and the Vatican museum just across the river.
Take another day to ride the bus to the Baths of Caracalla, and then continue on to the Christian catacombs on the edge of town. As a final touch, my kids loved the Capuchin chapel decorated with human bones :)