If you're looking for an apartment near the centre of Rome, I really recommend casa in monti. It has enough space for 6 persons and a good air conditioner, even for hot days! The location is great, since it is near to the main train station "Termini" and throughout the day you can return to the flat because it is in such a good place. Fabrizio is a very kind host and always replies very fast. For the last day we could leave our luggage in the apartment and grab it before going to the airport.
You should also try the restaurant vis-à-vis, they do a really great job.