Another post said it: try something central.

We were lucky enough to be near the main station.

For JustJenny, from the airport there is a train direct to the main central station , it's easy to find in the airport, quick and far cheaper than taxis!
Their fares seemed to be dependent on the way you look!
Must have looked like a pair of millionnaires then ??!!

Contrary to another forumer we found the bus service to be very good and easy to work, we did not try the undergroung though.

Generally speaking hotels in Italy are not excedingly good value for money so do "shop" around.
We rely a lot on Trip advisor for the comments and we book with either E-bookers, Booking.com/hotels or Expedia.

Rome is such a beautiful and interesting city, I'd love to go back!