Shopping can be somewhat difficult in Kassel compared to the United States, but most of the good shopping is located close to the Rathaus so if you get off the Strassenbahn around there you can do most of your shopping.
I found a good place to buy all of the stuff I needed for everyday things could be found at Muellers. It is somewhat like a Fred Meyer's or Target.
The best place I found to buy clothes was at the H&M right across Muellers located at Koenigsplatz. They have the best prices and clothing in my opinion around Kassel.