I pay $30 including tip at Cole's Salon for my daughter but she only get's a haircut twice a year or so because she has longer hair now but they do a AWESOME job.
My second choice is Kid's Hair I have gone to several locations and always specify when making the appointment if I can have the manager cut it. They do a really great job too. It's gonna cost you about 15 bucks but it's worth it.
My daughter has super fine hair too and the best haircut that works for her is a inverted bob stacked in the back it's easy to care for and has the appearance of being thicker than it really is. This hair cut does require frequent trims like every 6-8 weeks though.
I have tried cheap places like Fantastic Sam's or Great Clips and I've been extrememly disappointed with the quality of cuts.
I am a single mom financially challenged but when it comes to hair cuts I'm extrememly picky so I'd rather pay a little extra and maybe not go in as often but have a good cut.