lastminute.com has the EDI Sheraton for GBP 99 and the Balmoral (great hotel, great location-right in the middle of everything). for GBP 98. If you want really cheap and stay near the airport try the Quality Inn. No-nonsense hotel, but charming bar staff and some rooms have a lovely view of the runway.

Dont just do the run. Take a look at Edinburgh, its a great city!