Google Maps puts FCO
terminal on the north side of the airport, which is untrue, since it's south of the airport.
I considered staying there a few weeks ago (and finally choose another hotel more far away in Isola Sacra for Budget reasons), and looked into that. It's actually around 4 to 5 kilometers.
While it's doable to walk, it will take you one hour. Make sure to print out a map as there are a lot of motorways you can't use as a pedestrian.
You may rather take the hotel Shuttle,although I believe they charge quite a lot for it. That said, a taxi wouldn't be cheaper.
You could also take a regional train in direction Rome, and change at the first possible station which is shared by the trains to Fiumicino town, and the go back from there to Fiumicino town station, which is near the hotel. I believe they might be Fiumicino city busses, too.