Sounds like a good amount of time to spend in Rome and it will leave you wanting to go back!
I've been there twice now and loved it both times. There are so many sights to see.
We downloaded a tour from the internet for £10 from walkontours which takes you on an Angels & Demons tour. It goes (amongst other places) to the Pantheon, St Peters Square, Trevi Fountain, Piazza Navona, Castel Sant Angelo, and gives you step by step directions of how to walk to each place - very good as you do it at your own pace!
You should definitely spend a good amount of time at St Peters Square and the Basilica. You can climb right to the top of the Basilica (not for the feint hearted, but well worth it). Also allow plenty of time to visit the Sistine Chapel.
Try and find restaurants that are away from the main touristy sights as you will find them true Italian then and not overpriced bad food like some places we noticed!
Also, make sure you've a comfy pair of shoes and some sunblock!!
I would like to add a wonderful spot nearby Rome, called Tivoli. Try the Hadrian's Villa and the magnificent Villa d'Este (UNESCO World Heritage sites)
In Rome, besides all the places already explained I liked the catacombs very much, since you know a bit more about the history of our religion and the first Christians. The only inconvenient is that they are located a little far away from city center.
sorry I wasn't online for a few days. In half day you can visit colosseo and fori, included Vittoriano (bus from Termini station, then you can walk to colosseo).
Vittoriano closes at 17.30-18 (i don't remember exactly).
you can cut off aventino hill and visit trastevere in the night (it's a nice place full of restaurants and cafes).
in trastevere quarter a good pizza it's at Pizzeria ai marmi , viale trastevere.it's very crowded by romans, pizza it's good and cheap.
obviously you'll be on rush every day to visit everything...but you can consider 3 days as a taste of the city, and come back if you like it!
I really want to do the catacombs this time . . . does anybody know / remember how to get to them from, say, Termini?
Although I've been to Rome a few times over the years, I've been to the catacombs only once in my life -- and that was about twenty years ago! -- so I have no recollection whatsoever where they were or how to get there.
Just got back and was in Rome for 2 days. (Wish we had a little more time!) There are several different "double-decker" busses that run around Rome and stop at just about all the attractions. You can get a 24 hour ticket for (I think) 15 Euro and then ride to whatever you want to see, get off, enjoy the site, and then catch the next one to the next attraction... (Please note that the busses are colored and that the ticket will only work for the colored bus you initially buy for.)
3 days... it's a little for a city like ROME but I understand you can't stay more I found you post just now and i decided to write you and let you know this website: http://www.romeroma.com/Rome/ Hope this will help you to organize your itineraries around the Eternal City. I would like also to invite you to visit my fotogallery about Rome where you can find pictures of all this places that we are talking about and other places that are for sure worth to see like: Villa Borghese, Via Appia Antica, Villa d'Este, Villa Adriana...
Enjoy yout trip and you'll see that this 3 days in which you will see the most famous Roman symbols will be like an appetizer! Later you'll need more and more of Italy
Salutes from Rome!
[ Edit: Sorry, no promos please. ]
Not sure if you are into castle...
Can go for the Saint Angelo Castle...
I don't know, maybe this suggestion has already been made, but don't forget EUR to see some traces of Italy's infamous fascist past. The neighbourhood ironically is very agreeable, and there's also some fine churches on the way south. Also, cinecittà (Italy's Hollywood) is interesting if you're a movie buff.