I haven't been to most of these shops for years, so hopefully my descriptions are up-to-date.
Glad Creations has been around for decades and is packed with a wide range of really wonderful fabrics. They also have lots of quilts for sale, notions and books. They are fairly close to the downtown area, although you would need a bus or cab. Although historically they have tended towards the traditional, they usually have lots of batiks.
Bear Patch is located in one of the northern suburbs. They tend to be very traditional in their fabrics.
Twin Cities Quilting in Roseville is closer to downtown than Bear Patch. This is a smaller shop geared towards modern quilt design and fabrics that lend themselves to modern quilts.
Not really a quilt shop, but a fabric shop that carries a *lot* of quilting fabrics is S. R. Harris. They have a huge warehouse (measure and cut-your-own fabric) that includes quilting fabrics and just about any other fabric you can imagine, including silks and home dec. The warehouse is located in a far north suburb, probably too far. What I would recommend, though, if you are fabric shopping is their new store in Burnsville (a southern suburb). They are more like a regular fabric shop in that they measure and cut your fabrics for you. Last year when I was there they had a large range of good quality batiks for $7/yd plus aisles of other cotton fabrics for quilting. Here is a link to their website:
http://srharrisfabric.com/