Theres a municipal campsite at Stromness I can recommend, can't remember the price, but it didn't upset me at the time. Not too long a stay through. Its as close to Brodgar as Kirkwall is though.
Not too convienent, but very lovely is http://www.wheemsorganic.co.uk/ which has a bit of camping and a slightly zaney, ramshackle but cheap bunkhouse that you can also book for yourself as a self catering flat (sort of). I'd imagine Mike at Wheems would do a deal for a longer stay in the field, but its a bit of a trek to get to Brodgar from there.
Both very nice places to wake up in the morning