+1. I would suggest staying near Placa Catalunya, as the airport bus stops there, and many sites are within walking distance. You might still be able to catch the bus with your late arrival time, but check the Aerobus website.

Not sure if you would have checked luggage. If you do, the lockers in the airport are convenient, and I believe open 24 hours.

The barcelona-tourist-guide.com website helped me a lot on figuring out logistics when I was researching for my trip.