A great place to stay very close to the city center which is Roma Termini station. Stefano is an amazing host and is always willing to help and make your stay as comfortable as possible. He offered some really nice tea and cookies and has a great collection of CDs and DVDs as well if you are interested. We enjoyed our stay very much and would have preferred a harder mattress but it depends on one's individual choice. It was a bit too soft to our liking. Stefano has a guide written on his Airbnb account which you can follow for some really good food and for some hangout places around the city.
Lastly, I would like to add that Stefano is really silent and low-key as a host. Sometimes you wouldn't even know if he is in the house or not, which we liked very much. We had a very pleasant, calm and enjoyable stay with Stefano and would recommend his place to anyone planning to visit Rome.