http://www.stargatehotels.com - Reasonably priced at high season, OK.
http://www.hotelturner.com/index.htm - on Via Nomentana, 10-15 mins to Trevi fountain. Website makes it look far nicer than it is. But you'll probably spend most of your holiday in Rome walking about.
Most places are within 30 minutes walk of the main bus terminal in Rome (Termini) so could be best to find a place to stay close to there. Full of hotels and well connected, but not great otherwise.
Another option is to find somewhere in the Centro Storico (Pantheon/Piazza Navona/Campo Di Fiori). Great food, sites, pubs, and right in the middle of things. Reasonable price might be a problem. Area around the Vatican is also a good option.
You can do Pompeii in a nice day trip, although it takes some time to get there so is a full day trip. Bring an umbrella (there is no shade there, so it makes it more pleasant on a blisteringly hot day). Alternatively, do this day trip during off-season and in less heat. Also could do this trip via a night's stay in Napoli (supposdely fascinating if not relaxing), and/or another in one of the towns along the Amalifi coast such as Positano or Amalifi or Ischia.
Alternative day trip possible to Ostia Antica, the Roman river port. Adam (cthulhu) recommends it as just as good as Pompeii but less than an hour from the city.
Sistine Chapel is morning opening only, and queues are massive so get there early. Not all brickies recommend this, as there is a long walk around heavily decorated corridoors through crowds before you actually reach the chapel, and it has the potential for anti-climax. (Alternatively, it is still quite impressive!).
Other options for visits include the Colesseum and the Palantine (both covered by the same ticket, you can save time if you buy at the Palantine).