Your best bet is to stay over Carl. Me and the misses tend to stay over in the Premier inn at Durham, it's cheap bang in the center and only about half an hours drive to Beamish. If you are going for a night over I would spend the first day in Durham, the cathedral and town center is pretty nice to walk around. Second day I would hit Durham.
Beamish is split in to different parts, your better off hitting the coal mine first as it gets rammed. Make your way up to the farm house, then take the tram in to the town for beer, sweets and town attractions, a short walk on to the fairground and steam train. I would then get the bus down Pit Village again for the chip shop, try get there before prime time lunch or afterwards as it's very, very busy. Pit Village all so has the school, church, cottages and band stand. I would suggest visiting the farm last as your legs would have had a good workout by now and you'll probably be feeling it.
If you want to catch something to eat before the drive home I strongly recommend http://www.beamish-hall.co.uk/stables