have a look at the premier inns or travel lodges we got a room for £29 afew weeks back, just outside edinburgh..

Google "cheap bed and breakfast Edinburgh"
Some friends said that the Valantine on Gilmore place was decent at about £20 ppn

You could see if there are any apartments available, they can work out cheaper but I doubt it at this late stage and given the time of year

I stayed at some on the Royal Mile, they were excellent and cheap, worked out at about £35 each for a 2 bed