A cheaper good hotel to consider is the Exe Hotel Della Torre Argentina
http://www.tripadvisor.com.my/Hotel_Review-g187791-d258994-Reviews-Exe_Hotel_Della_Torre_Argentina-Rome_Lazio.html
We’ve stayed there. It’s got a VERY convenient and central location (between the Pantheon & Campo di Fiori), but it’s on a VERY large, busy boulevard-- right on Corso Vittorio Emanuele II. The rooms in the back (not facing Corso Vittorio Emanuele II) are quiet. The rooms facing the boulevard have sound-proof glass in the bedroom window, but not in the bathroom window (but you can just close the bathroom door). The hotel is less than a 5 min walk to the Pantheon (that’s inclusive of time to wait for the crosswalk on Corso Vittorio Emanuele II). The restaurant Vecchia Locanda that I recommended earlier is in an alley right between the hotel & the Pantheon.
The bus stop for the public bus is RIGHT IN FRONT of the hotel, and the bus goes right to Termini (the train station), so it enables cheap access to the train station and therefore cheaper access to the airport. The rooms are comfortable and the bathrooms are nice. Just don’t opt for the breakfast-- it’s awful. But there are cafes everywhere as soon as you walk out the front door.
The hotel is a good value and I would stay there again, especially if the kids came along and we had to spring for more rooms.

I also kept a credit card, drivers license, and some Euros in a buttoned up pocket, that was easy to get to. I figured that if that was stolen, no big deal.