Have a very early flight out of Rome. I don't really want to spend the night in the airport -anyone know of hotels close to the airport? Where do flight personnel stay?
(Fiumicino Airport)
This answers your question http://www.roninrome.com/2009/03/15/getting-to-fiumicino-early-in-the-morning/
IMO, you can also stay the last night in Rome and have your hotel have a taxi appear as early as you need. This is done all of the time and is quite dependable. The hotels at the airport know why you are there and are often a bit more expensive and with less service. The taxi ride shouldn't be more than 43Euro including luggage.