Hilton Garden Inn Rome Airport {ITA}
Just had a peek at the HGI e-letter and FCO (Rome airport for the seach engines) is set to get a HGI. Scheduled to open year end and it located by the cargo area.
Free shuttle bus offered to the city, Parco Leonardo shopping centre (claimed to be the largest in Italy) and the local harbour. Wasn't explicitly stated but I assume there's shuttle service to the passenger terminal too. Parking is a bit stiff at EUR 20/day.