Well - our very first trip overseas in '08, we went straight to Rome for 5 nights. Yeah - it was intense - especially the shuttle van ride from the airport to the B&B (they are INSANE drivers!) but we quite enjoyed it. You are lucky to have a week. We took a day and did a side trip out to Appia Antica - walked the ancient Roman Road, visited the catacombs (we didn't get as far as aqueduct park, but I hear it's lovely and you can rent bikes to bike around) - it was a nice break from the craziness of the city. On our 2nd visit to Rome, we did Ostia Antica, which was also a nice change of pace.
So my advice would be to schedule at least one 'quiet' day in there - and just enjoy. Stop for gelato, sit and watch the world go by at Piazza Navona or by the Pantheon. If you are early risers - it's a good time to go visit something like Trevi Fountain or Spanish Steps if you are close by - to avoid the crush that will be there by mid-morning. We stayed a block away from the Colosseum on our 2nd trip, and my mom and I would be out at 7am for a walk by before the hordes descended. We'd walk down the street and pop into churches - it was great.
Just wanted to add - we found it intense because it was our first trip overseas - learning about the trains, the metro, the language, how to cross the darn road without getting killed! And arrival day we were coming off an overnight flight to London and connecting to Rome, so toss in some jet lag and disorientation as well.