Neighborhoods near airport in Rome

Personally I would stay in Rome your 1 night, do a little site seeing and then have your hotel arrange for a private car ride very early in the morning to the airport.
No personal desire of mine to stay in the Rome suburbs just to be closer to the airport and save 20 minutes of sleep.

Stay in Rome itself and enjoy the late afternoon and evening there. You should not have any problem getting to the airport early enough for the flight. A private car service for four will be, in my opinion the best way to go. We can not say enough good things about Rome Cabs. It is a private car service (not a cab company) but only cost about 10 Euro more than a regular taxi. We always use them and have always been very pleased. Go to romecabs.com and see what you think. We usually send an email and they answer us with a quote within 24 hours. You do have to pay cash (Euros) and the end of the journey but not in advance. The problem with having the hotel make arrangements is that you might wind up with a regular cab, a car service, or the desk clerk's brother in law. Happened to us once but there were four of us and only one brother in law so there wasn't a problem.

As long as the brother-in-law is driving a clean car, what is the problem?

I tend to think if the hotel has a decent number of rooms any driver accepting their trip has incentive to make sure they are on punctual and professional. There potential repeat business is far greater than mine.

The one time I did what I describe, I think my hotel used Rome Cabs. It was a private car and cost $10 more than a taxi ; had to pay cash, etc... so seems to be similar if not the same. They were very professional and everything was perfect on both pickup at airport and early morning pickup to the airport when departing Rome.

Either way get the hotel involved if staying at one, they can help you in the morning if they know the driver is coming.

My first time to Rome, I had the unfortunate pleasure of using one of those "illegal" taxis that hover at the airport arrival area, not doing that again so will stick with Rome Cabs or hotel arranged drivers if in Rome again.

mreynolds, your points are well taken and are certainly valid. To answer Frank's question, that particular time the car and brother-in-law left a good bit to be desired with regard to appearance and professionalism. While that may have been an exception to the general rule, once burned twice shy. Just my opinion.

AC it definitely sounds like an experience.
As long as you made it to the airport on time I guess it adds to the charm/culture of the trip.

While completely different I have had other experiences in Italy that were quite unique, all ended well and are good stories and things you remember the most looking back on a trip.