Mr. Rududu and I like to explore places in depth. This month we took that idea to its logical conclusion and stayed in Rome for over two weeks.
That September and October may be the nicest months for visiting Rome is no secret judging by hoards of other tourists. If you are looking at something famous in Rome, you probably won't be alone. Here for example are the crowds approaching the Sistine Chapel. (Being in the chapel was better. Most people don't stay very long.)
We rented two different Roman apartments through a site I just read about this summer: airbnb. It's a combination of B & B agency and social networking site. Renters rate the places they stay and owners also rate the guests. Some people rent just a room or even just a sofa and there can be back and forth communication setting up a rental. One pays in advance but the money is kept in escrow until 24 hours after arrival, providing some protection against scams or misrepresentations. We opted for entire apartments and loved both places that we stayed. One was near Trastevere and is owned by David, a very helpful guy that walked us around the neighborhood to orient us and gave us printed instructions for using the public transit system to get to all major tourist areas. The owner of the second place, Luca, was charming and his apartment was centrally located and very spacious. Here is a photo of its living and dining area.