Most of the main tourist sites are in a very central location, thus making it easy to walk around and visit everything. Contrary to popular hearsay, Rome is not another super expensive city. Things are reasonably priced for Europe and if you look around, it is not too hard to find cheap deals. For places to stay, check out the hostels near Termini Station. The prices are great and this is a central location making it easy for you to walk or catch the subway.
Just like in most cities, the city center restaurants can be pretty touristy: small portions, kinda pricey, and not that "homemade" taste. You have to visit the Trastevere neighborhood. Even though it is a striving bustling neighborhood, it has a heap of great eats at cheap prices. My favorite restaurant is Ivo; a stupendous restaurant nestled off the main drag. For 6-9 euros (dinner prices at that!) you will enjoy an authentic Italian meal cooked to perfection in a cozy but vibrant setting.
Believe the hype! From the Coliseum to the Spanish Steps, from Trevi Fountain to the Vatican, from the Patheon to the best pizza you'll ever eat outside of New York, Rome really is just an amazing city that you really must visit.
Some pictures contributed by N.M.