This is the way to go. I would try to find a hotel in Jersey City, Secaucus East Rutherford and take the train/subway to the game. Probably your cheapest/bang for your buck alternative.Just booked a room in East Rutherford. Subway to the game.
I don't know what the flight situation is for you guys, but don't think LaGuardia is the only option (Newark may be better).
Check this for those on a budget for a hotel: Hotels.com
Hope to see you all there!