Hi

When are you going? In off season your hotel money goes alot further. The Hotel Panda - http://www.hotelpanda.it - is centrally located. The historical centre is where you want to be to fully appreciate the city. Getting to the car rental shouldn't be a problem. Plenty of transport options.

There good hotels which are both near the Termini station near both the main sights in the city centre as Colusseum or Spanish steps.
I suggest you should have a look on this http://www.hotelraffaello.it right behind Major Virgin Mary's Church

I recommend Hotel Milani near Termini, one street over on Via Magenta http://www.hotelmilanirome.com/

My sister stayed there based on recommendations and she was very pleased. More importatnt than staying close to a car rental place is staying convenient to public transport. This hotel meets both at a good value.

BTW, I would NOT recommend you rent a car from Rome. Use the train to get to Florence (so easy and cheaper!!), bus to San Quirico and rent there.

I too suggest taking the train to somewhere to get the car, but certainly not Florence with a 2 hour backtrack to San Quirico. There is no car rental there anyway. I suggets going to Orvieto to get the car---the Hertz/Autoeurope outlet is near the station. From there, I suggest the scenic route via SS-2 to Bagno Vignoni and San Quirico.

If you look on booking.com and venere.com you can search for a hotel or b&b in your budget for your travel dates and see what is available. You can read up-to-date guest reviews and find out if the hotel is noisy or quiet. It can be noisy anywhere in Rome if your hotel is near a bar/restuarant with outdoor seats or a bus stop. So read reviews if you want a quiet hotel.

It is better to pick a hotel that has the things you want -- wi-fi, air con, etc -- than to worry too much about being right next to some specific sight or the the train station. As long as you are in the central neighborhoods (Spanish Steps, piazza Navona, Vatican, Monti, Termini) you can get around to sightsee and back and forth from the train station. If you need to take a taxi once or twice with your luggage, it is better to pay for that once or twice than to stay in an uncomfortable hotel where it is hard to sleep.