Rome is a fascinating city. It is also fairly compact. Everywhere you walk, there is history. As far as what to do, I recommend the major sites for first-timers: Colosseum, Roman Forum, St. Peter's basilica, Vatican museums, Spanish Steps, Trevi Fountain, Pantheon, the Catacombs, Piazza Navonna, Campo di Fiori.

For hotels, Rome has a wide variety, ranging from hostels to 5-star deluxe. Depends a lot on location and what you deem is reasonable. Full service hotels include tax and breakfast in posted rates.

A word of caution. While all major cities have problems with petty theft, Rome is especially notorious. Be aware of your belongings at all times and avoid groups of children who come up and surround you, especially around tourist sites. They are professional pickpockets who will distract you, then clean out your pockets and purses before you know what is happening. Enjoy!