I recommend getting a Rick Steves Rome guide book. If you stay in the old part of the city there are many things you can walk to and see on your own.
You may also want to get a 3 day Rome Pass. For 30 Euros you get admission to 2 Museums or Archaeological sites and discounts on any others you visit. You also get free use of any public transportation (bus or Metro). It is worth it if you are going to visit the Colosseum and Forum on you own because admission to these alone is over 15 Euros. The passes can be purchased at any TI in Rome or at the Airport.