When you say you're staying near the chapel, do you mean the Vatican? Actually inside, or just somewhere near? Doesn't matter really, everything is within walking distance.
We were there this time last year for our belated mini-honeymoon, and I'll give you these tips:
1. Get used to walking. We were based off Piazza Del Popolo, and never felt the need to use any other transport at all. Even walking right down to the Colosseum wasn't an issue at all, and there's some amazing architecture on the way if you like that kind of thing (check out the law courts and the parliament buildings, stunning).
2. Don't f*ck around in the Vatican, they have zero sense of humour. We saw two Jap girls booted out for taking the traditional peace sign photos they love so much whilst in St Peter's.
3. Get to the Vatican museum early, and spend all day there. I found the Sistene Chapel really dull, but each to their own. Their collection of tombs and carvings from BC are incredible and you can touch them, if you dare. Astounding.
4. Eat the biggest breakfast you can, 'cos there ain't a whole lot to eat there! You think I'm joking, but unless you're on a huge budget the restaurants are mega bucks and not worth bothering with. We ate big in the morning, found a small pizzeria for lunch, then basically just ate the free bar snacks and got pi**ed in the evening.
5. Colosseum is not that impressive, but the nearby ancient Rome ruins are just indescribably superb. Worth a couple of days alone, and the history there is something else. HINT: Find a tour guide with a small group, then follow them around and eavesdrop for cheaps
6. YOU ABSOLUTELY MUST GO VISIT the Keats - Shelley house. Located just by the Spanish Steps, it's a cracking little museum that no-one really knows about but again, the culture there is just wonderful.
7. www.romecabs.com is the place to book your transfers from, if you've not done so already. Excellent service, good pricing, and trustworthy as anything.
We love it there, and like Lee says I'd go back just to hang around and soak up the atmosphere. Wonderful city.