We stayed at and would recommend the Hotel Aberdeen, which is near the train station and also near a bus stop where you can get a bus to all the sights. It was under $200 a few years ago when we stayed there, but don't know if it still is. The staff is very nice and helpful. Rick Steves recommends it. Here is the website (or you can check it out on TripAdvisor or Booking.com)

http://www.hotelaberdeen.it/

Before you look for a hotel for one night in Rome, do you really have to stay in Rome before heading to Sorrento? I see in your other thread that you are staying four nights in Sorrento. I don't know where you are heading after Sorrento, but if you are heading back to Rome before flying home, you might be staying in Rome for the second time, perhaps unnecessarily.

Good thought on staying in Rome. We have not booked our airfare yet as the rates are so high. Ideally we would like the best airfare. Flying into Florence and out of naples or rome. Maybe I should look at flying in and out of rome. Right now airfare is between 1600 and 1700 per person.

Simple, clean safe near Rome Termini reasonable rates
Hotel Diana - Via Principe Amedeo, 4 +39.06.478681 internet point, roof garden
Hotel Torino Via Principe Amedeo 8, Phone 39-06-4882247 Free Wifi roof garden

All are typical tourist hotels, all serve great breakfast and have decent comptent staffs and all are located less than a block from the terminal and if you fly in and out of Rome all are also a block from the airport shuttle bus which costs appx 4e and departs every 1/2hour. Under the terminal is shopping and Conrad grocery (called the drugstore) should you require anything.

Re Naples: its been my expereicen they are seldom and decent deals flying in or out, Rome will give you a better chance of getting a airfare deal.

You have to decide whether you want the best airfare (with an unstated assumption that it would lead to the best overall expense) or the best possible overall trip expense and itinerary within your constraints. The two are not always the same.

Some plan by getting the best airfare, then best accommodations, then best ground transportation assuming the sum of all yield the best overall expense picture. Compare this to integrating airfare, the accommodations, and the ground transportation in different ways to see which yields the optimum itinerary with the associated cost. Even if one item costs more, if it contributes to more than compensating savings in other area, would you not be better off overall?

Are your real destinations Florence and Napoli and Rome is just an airport for this trip? One option, if you have to use FCO, is to travel directly to Florence or Napoli upon landing and minimize your stay in Rome just to synch to your return flight. You have several airport combinations, NAP,FLR,FCO you can try to compare trip durations, layover risks, arrival time, the cost, and how well these airports integrate into your itinerary.