Our plane departs FCO at 6:20 AM. Should we seek a hotel closer to the airport the evening prior our departure to help avoid the $80 taxi fare? It there a problem with transportation that early in the morning?
Given the early hour of your flight, I'd probably consider staying close to the airport. One location you could consider is the Rome Airport Hilton, which is right at the airport. You can walk directly to the Terminals via a covered walkway. Happy travels!
Augusta, we've often flown on the 06:20 KLM flight to AMS when connecting to the States. We lived in Rome so we always stayed in-town and booked a shuttle or called a taxi. Yet, I understand the need to stay out near the airport. You might look at this link for more suggestions: The Best Hotels and B&B's near the FCO Airport
Rome Airport Hilton gets a second from me. Used it twice for early morning flights. In the hotel. You can use a luggage carrier to push your bags to terminal or their shuttle.