What hotel is recommended at Fiumicino for the night before a flight out?
I always stay here. There are others some distance away from the airport, which would require either a taxi or the hotel shuttle (if available), but I prefer the Hilton at the airport, which is basically 5 minutes' walk across from the terminals using the aerial covered bridge.
It is not a perfect solution, but it is the rare case of a hotel from which you can, using a special outdoor elevator, walk directly from the lobby towards the departure concourses. No shuttle bus needed in the morning.
We found it noisy, long lines to check in, and the restaurant closed too early. But the rooms are normal modern Hilton quality. Don't take a room that backs up on elevator machinery.
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Glad you got your answer!
Here is an option for you. Hire a private shuttle like www.suntransfers.com and stay in the city center. This way you can get the benefit of enjoying Rome one last night. The shuttle can pick you as early as you like. I have scheduled pick ups for as early as 3:30am with no issues. Also, at that time of day there are no traffic issues and you can get to the airport in like 30-40 minutes.