Fair price for a used beginner guitar?

My teenage daughter wants to learn guitar, which I totally support, but I know how teenagers are. If she sticks with it, I will buy her a new, quality guitar. On the other hand, I don't want to sink too much into a whim that might not last past a couple of lessons (as teenagers are known for). So what's a fair price for a used one? Doesn't have to be top notch, just enough to gauge if she will stick with it or not and then I will upgrade.

Also, if anybody in the metro area has a used guitar to sell...............