Sounds like you'll have 2.5 days in Rome, so I think you can see an awful lot if you're so inclined. I'd suggest picking up a travel book (I love Rick Steves' series) and taking a look at the suggested itinerary for a 3 day visit. Cull out the things you don't want to do and spend the extra time at the places that most jazz you or simply get lost walking the streets (which is very easy to do in Rome).
To me, the Vatican is not to be missed. I'm not Catholic, but the history and art are beyond description. I agree with trueblu - buy your tickets online to avoid the massive lines. Personally, I think the Vatican is worth a half day of your time, even on a short trip.
As long as you're staying in the old city, you're within easy walking distance (or a very short cab ride) of the Forum/Colosseum/Palatine Hill (all adjacent to one another and one ticket gets you in to all three...buy your ticket at the Forum since the Colosseum lines are 10x longer for the same ticket), Trevi Fountain, Spanish Steps, Pantheon, Piazza Navona, etc.
The food is amazing, as are the people, sites and history. Frankly, I think no matter what you do/see, you'll be looking forward to your next trip as soon as you leave.
Enjoy!