Couple of practical points, if this is your first visit to Rome.
You can think of Rome as a series of concentric circles, more or less centered on the area around the Colosseum, the Forum and the Palatine Hill. Most of the places visitors want to see are within reasonable walking distance of each other - up to 30 minutes, and it's an interesting city to walk around in - but Rome is hilly and a lot of the streets in the older parts of the city are cobbled. I'd suggest taking good walking shoes. It's not really 'heels' territory!
The underground is fairly useful, but there are only two lines. They intersect at Termini (main rail/bus hub), and there are no other connections between the stations, so it won't always take you where you want to go. Buses are a good option, and you can usually tell the driver or other passengers where you want to get off and they'll help. You can get combined underground/bus passes, and these are worth it. Taxis are fairly expensive.
Have a great time and remember to throw a coin into the Trevi Fountain, if you want to ensure that you go back!