There aren't any shops I know of downtown near the center, unless brand new ? - but there are several north of downtown. The Quilt Store and Sew Much More are both on Anderson Ln off I-35 N, and Honey Bee Quilts is off 183 N (Research Blvd) at Anderson Mill Rd / Jollyville. There's also a shop up in Round Rock, can't remember the name ... and the ones mentioned prev down in New Braunfels. Also a very nice shop up in Georgetown - Poppies ? Haven't been there in awhile ...
Too much to see in a day, that's for sure ! Have fun ! :)