I have two suggestions but have only been to one of these salon's. The first place, that I have been to, is on Blossom Hill across the street from Sears at Oakridge Mall. They will give you a piece of her hair and a little certificate, but they charge like $18! However, so far worth it to me because they have these great little cars the kids sit in, there is always a movie playing, and a little play area while you wait. They also usually have a jumpy house that I tell my kids they can go in if they behave while getting their hair cut.
The other place, the I haven't been to but am going to try the next time because closer to my house, is on Meridian and Branham by Petco (or it could be a Petsmart). I've only looked in the window there recently and they also have little cars the kids sit in, etc. Not sure if they are cheaper.
Anyway, good luck!!!