Well lucky for you... I lived in Italy for 4 years and still have all my hotel info!
San Pietro Rooms is a very nice 1600 century hotel with marble floors and sweeping balustrades. Only 2 blocks from the vatican, it is an exceptional hotel because you have your very own bathroom, and continental breakfast inclusive and the reception desk does speak English. If you have any military experience, the USO headquarters is only 2 blocks away as well and they offer discounted shore excursions that pick you up from the hotel and bring you back - excurions to the Vatican Museo, the colloseum and Forum, and even Pompeii!!! As I recall a double room that slept four cost about $100 euro a night and that was a few years back. I'm sure the rates are much more now, but believe me you won't be dissapointed, especially since everything to see is so centrally located.
Website you could visit:
http://www.italmarket.it/rm/sanpietrorooms
email contact: sanpietrorooms@italmarket.com
Telephone: 39 - 06.3725528 or 39 - 06.3725617 Fax: 39 - 06.3725463
Address:
Roma - Viale G. Cesare, 62 (Ang. via Barletta)
Scala A, int. 1, primo piano
Economy Stay:
Now there is one other place that I stayed on a budget and also not too far from the vatican, and owned by an old Italian lady named Franca Fondi; however I question whether it is still in operation.
Hotel Benjamin - via Boezio, 31 - 00192 - Roma - Italy
Telephone: 39 - 06.68802437
Note: The Benjamin shares bathroom...