Handicrafts are available everywhere although many items are only found in a single location. Many cities have a special OTOP shopping area specializing in products produced under the One-Area-One-Product program, a great way to shop Thailand from a single location.
Batik studios and Art Galleries are a fun source of interesting Handicrafts found in all tourist centers, sometimes with several available within meters of each other, and at other times simply by themselves. It's well worth exploring to see the differences in what's available and taking the time to find the art that's exactly what you're looking for. Many large Shopping centers offer a wide selection of Handicrafts.
Many shops will help you prepare to carry your purchased on your return trip, or help to arrange Shipping.