The Esquiline
Through the offices of RealRome.com, we rented "apartment Giovanni Lanza" at the intersection of Largo Brancaccio, about 2 blocks south of Santa Maria Maggiore Church. The apartment was on the fifth floor (US, or 4th floor Europe) of this wonderful Pianoforti building (they sold beautiful grand pianos on the ground level).
It was a wonderful apartment, certainly the best we've ever rented in our European trips. Two bedrooms, two baths, heat we controlled, windows we could open, comfortable furnishings, nice big kitchen. Even an elevator (although we persevered and took the stairs on most days).
RealRome (and Tim Pearson) were extremely cordial and helpful in the rental process. I recommend them strongly.
Across the street from the Pianoforti building was a bancomat (ATM), post office, laundry, and the Brancaccio Museum of Middle Eastern Art.
In the apartment, we had satellite TV with US and European stations. We were intrigued to watch Al Jazeera TV, Fox News, and the Simpsons, almost interchangeably. And FashionTV lasted 24 hours a day!
The apartment was very nicely furnished, with comfortable furniture, good kitchen equipment, nice beds, and shutters on the windows!
When we arrived, Tom was coming down with a cold, so I "volunteered" to sleep in the room with twin beds, so he could get some rest. The room was very pleasant, with a bookcase, giant chiffarobe, work table, and night lamp.
The floors (of marble) were particularly nice. I was afraid they might be slick and cold, but they were very comfortable. For the record, the bedrooms also had internal air conditioners, which would be extremely important in August!
If you looked out my window, to the left you would see the street stretching towards a park called "Vittorio Emmanuelle," where we found an incredible food market. Toward the right, the road led to Via Cavour and then to the Colosseum and Forum. You can ALMOST make out the Vittorio Emmanuelle monument at the far end.
This view was particularly fetching on New Year's Eve, when thousands of people were shooting off little fireworks and waving sparklers out the building windows, up and down the street.