We just spent 4 days in Rome with children and had an amazing time.
Our highlights were:
1) Crypt of the Capuchin Monks - if your kids want to see bones...this is the place. The monks have used bones to create art work. Cost is a small donation. My kids were disappointed with the Catacombs of Priscella as they wanted to see bones.
2) Ostia Antica WAS another huge hit. We used a metro day pass and travelled 30 mins on a train to get to it. The kids loved exploring the ruins.
3) Climbing the Dome of St Peters - this was also amazing. The kids loved counting how many steps to the top. A little tip - get there at 8am as there are hardly any queues.
4) Gelatti from Pellacchia (Via Cola di Rienzo 103 - Vatican Area). We all loved the Caramello flavour and they are so big!!!!.
5) We downloaded and placed on our ipods - information on many of the sites. We downloaded a kids version. This saved us money as we didn't do the tours. We just walked around with our ipods.
6) Our apartment in the Vatican area was huge. There was 7 of us. We used rentalinrome and they were great.
7)I would also recommend using a taxi to transfer you to and from the airport. We used romecabs and they were great. It just took the stress off getting to and from the airport.