I spent a few days in Barcelona after my Camino last June...I'm not sure what accomodations are close to the airport....but I know there are a few hostels downtown...I stayed at and would highly reccomend Hostel Somnio
http://www.somniohostels.com ....which has dorm beds for 25 euro...they also have single and double rooms,...for a few euros you can take the subway/train from the airport to downtown....trains go every 30 minutes and the trip will take a half hour....if there is more than one of you travelling ...buy one T10 card and share it ...to and from downtown...it costs about 7 euro if I remember correctly..and it is good for 10 trips..hence the name ....I found the train is faster, easier and cheaper than the bus...
Let me know if you need more info...Barcelona is a great city..even if for a few hours!
Marilyn