Any recommendations for a hotel at the Barcelona airport the night before traveling back to the states?
I don't know how early your flight is but we've just stayed in the Eixample neighborhood the last night and taken the Aerobus to the airport in the morning.
We stayed in Gothic quarter a few weeks ago and got a taxi to the airport. 32 euros and took about 30 minutes.
Not worth it... the airport is very close to the city -for usual standards in other major cities- therefore there's no reason to "stay at the airport". It should take you under 45' to get to the airport by taxi, Aerobus or metro.