Women's abuse shelters would be more than grateful for your quilts. As much as I would love to have you send them to me, I know they would love them just as much, more. I have taken items that would seem insignificant to a lot of us....skeins of yarn, pattern books, hooks, needles....and you can't believe how welcomed they were.
I also took in extra sets of dishware, cookware, etc. The woman that go there for protection usually ESCAPE from their abusive homes with little or nothing, and these things mean so much to them. So imagine how much a handmade (by hand or machine...a HEARTMADE) quilt would mean to them. It would be something to warm them inside and out.
Don't worry about your family not wanting your quilts. Take them to someone who will treasure them. You can find the shelters usually by a phone number only, because they do not want the abusers to know where the shelters are. My dh has been allowed to accompany me there after a few trips, but they made sure he was one of the good guys first.