I've had a wonderful time staying at this apartment of Antonella's. She welcomed me personally and showed me around. After that she gave great advice on the city and was very helpful during my entire stay.
The apartment is situated perfectly both for walking into the old city centre or making use of public transport. And because it's near to Termini Station, I'd imagine it would be a good starting point to extend your travels further into Italy.
If you were to book a place in Rome, I would highly recommend Antonella's!