getting to FCO for an 8 am flight

This is where we stayed when we had an AM flight out of FCO to US

http://www.hotelrivierafiumicino.com/en/home-page.aspx

Would do so again. Shuttle service cost was very reasonable.

If you have an 8am flight it is most likely a domestic flight to somewhere else in Europe for your connection home so an hour and half to two hours in advance is more than enough at 8 am since it is not an international flight. Stay at the Hilton, it is connected to the airport and you can walk. Makes it simple.

Your 8am flight is certainly an intra Europe flight since the first flights to North America depart closer to 10am. That means you can show up at the airport around 0630-0645 am and be fine. Just stay at the same hotel downtown Rome and ask the hotel to book a taxi for 6am. The flat fee taxi fare is 48€, all inclusive.
You will be at the airport in 1/2 hour.

I would have voted with the "last-night-in-Rome, use-a-taxi" crowd but I know you say you don't want a taxi from Termini because it is too expensive. Are you sure that the €48 flat fee for the taxi plus less hassle not having to move hotels on your last day in Rome isn't pretty much a wash with the €20 or €30 taxi from a near airport hotel plus the hassle of moving plus being away from Rome for your last afternoon and night, plus the cost of however you will get to your near airport hotel?

Traffic (or actually the lack of traffic) at that time of the morning will make the trip from Termini area fast and easy.

I have stayed at the airport Hilton before and taken a taxi to the airport at 6 AM. Both worked out fine but my preference is to stay in Rome to avoid changing hotels for one night.

I was wondering about this myself, since we have a 9:15 flight. I decided that the cost of a taxi made more sense than packing up and moving for a single night, and for the fact that my current lodging choice in the center is about a taxi ride less than the airport Hilton.

I'll just throw this out...

The cheapest way to/from Termini to/from the airport is by bus; tickets are anywhere from 4-6 euro. Terravision, SIT or TAM:
http://www.adr.it/en/web/aeroporti-di-roma-en-/pax-fco-bus

If you have to be on the earliest bus to be at the airport in time to catch a flight, I'd buy tickets in advance for that time slot (check schedules for each service).

2nd cheapest is Leonardo Express train. The first one departs at 5:35 AM and arrives at 6:07. Tickets are 14 euro PP.
http://www.adr.it/en/web/aeroporti-di-roma-en-/pax-fco-train

If you do decide to ride the Leonardo Express on the morning of your departure, you can save time that morning by buying your ticket in advance (for example, the day before).

We stayed at the FCO Hilton before flying out in the morning. Even though you can walk to the terminal via the skyway, they offer a free shuttle to drop you off.

I stay at Hilton properties when I travel for business, so I could upgrade free to the Executive floor. We grabbed our breakfast in the Executive Lounge.

Being at the airport was worth the price for the peace of mind it brought. We also turned in our rental car when we checked in the day before. There's a free shuttle to downtown Rome and we went into town for dinner and a little sightseeing.

We stayed at the Hotel Tiber near the airport in 2014. Very nice, good service, restaurant on site with included breakfast. They offer an airport shuttle for a small price, back then it was about 6 euros. I'd stay again.