You are kidding, right?
Edinburgh goes into its fullest major rip-off mode at this time of year!
Someone once suggested you would be better off staying in Glasgow and training it. I now tend to agree - You can also do the same in Fife or East Lothian but the train connections are far better from Glasgow.
There are some more threads in this forum about Edinburgh in general and at Festival time that may be useful to you - Some had Hostels etc linked, which is about as cheap as you can get if they are not fully booked already.