Unfortunately, there are no LQS's near Palmer Center. The Quilt Store is a few miles north of there on Anderson Lane...wonderful shop.
If you're also going south of Austin, there are two wonderful shops in New Braunfels, about an hour south of Austin on Interstate 35. The Quilt Haus on Business 35 and Oak Leaf Quilts downtown near the Plaza (and near a fabulous bakery!).