I'm glad you are getting so good suggestions for quilt shops. I live in the next town over from Chandler and these are a few of my favorites.
Mulqueens - Mesa location at Val Vista and Main. They have a great selection of good quality quilting cottons at $6.95 per yard. They also carry many brands of threads, patterns and a wide selection of quilting tools, ruler and accessories. If you are into machine embroidery they also have a huge selection. (Can you tell this is my favorite "go to" shop)
Quilters Oasis - East Mesa on the Southwest Corner of Crismon and Baseline. (Out a ways but a quick drive on the 202 highway) Very nice shop with a great selection of batiks, civil war, and current fabric lines.
Quilters Ranch - Southwest Corner of Warner and McKillips which is not too far. A fun, well stocked shop with good variety. I don't go in too often so can't give you a rundown of what they currently have in stock.
Cottage Rose Quilts - Dobson North of Main in a log cabin type of building. She has a great selection of florals and blenders. Nice quality.
Cutting Edge Quilts - downtown area of Chandler on Arizona Street. Smaller shop but good quality and variety.
35th Ave Sew and Vac - two locations one in at Ray and Rural (not sure if thats Tempe or Candler) and other in Phoenix off the I17 and Northern. Ray and Rural is a nice quilt shop and another of my mainstay quilt shops. The Phoenix location is absolutely huge!!!!! and well worth the drive to shop. I believe they have the largest selection in the area.
Let me know if you need more information, I would be happy to help if I can.