Edinburgh will be VERY BUSY it is festival time. Everywhere to stay is likely to be booked.
If you do find somewhere go to the Royal Oak. It hosts the Wee Folk Club and has a great programme with a concert every night rather than just on Sundays.
If Edinburgh is full go to Dunkeld and the Taybank Hotel only an hour further North. ,or Stirling FC or Glenfarg FC or.... or... too many more to mention.

Try visiting Chester on the way up or down lots to see and hear. check outon the Folk Orbit site for venues ..lots and lots...