They do purchase used guitars but you won't get half of what it's worth. Your best bet is to sell your guitar on Reverb.com or even Ebay.
They greatly depreciate the value when you trade up or sell. May get more trade value vs cash. CL was mentioned, but FB yardsales or marketplace could be useful as well. Good luck!
Or try to sell on Craigslist. GC is a good place to buy used guitars from, but not for selling them to.
Thanks! Your answer is awaiting moderation.