What is the value of a 1917 liberty Standing quarter?

Its value depends on its condition, mint mark, and design. There's a list of retail prices at the numismedia website, among many such sites.

This coin has an interesting and somewhat bizarre story that accounts for the Type I and Type II designations. The initial design showed Lady Liberty with draped clothing only partially covering her torso - see it at the coinfacts website.

The prudes of the day* immediately got into high dudgeon and actually forced the Mint to recall the coin and issue a new design with a more "modest and proper" depiction; see it at the coinfacts website.

(*) not to say that there aren't plenty of current-day extremists who wouldn't go ballistic in the same way, sorry to say. There are loads of 18th-century paintings where Lady Liberty is in various states of undress but no one seemed to feel offended then. There's no way of explaining why some people get upset. I'll even bet there are a few who just can't get over the fact that underneath their clothes, all of us humans are actually naked, LOL!