you can forget most retail stores, only the actual corp. can make those donations and they don't!
Lqs are barely making it now, so doubt there would be any help there...
Like others have said, FREECYCLE.org for your local area is a good place to try.
I also go to my thrift stores on Tues at one and Fri at the other, they have a sale area and I buy the 100% cotton mens shirts for $.25! Do you know how much fabric you can get out of a 3xl long sleeve shirt???? and for that kind of money I stay well stocked on charity fabrics! Skip the womens shirts, too many seams, darts etc and they are never 100% cotton, they always have poly or spandex in them!