Here is one of my favorites and a shop that I actually made an effort to visit again just before I moved. I love their brightly colored woven baskets with the leather wrapped handles. They also have beautiful olive wood bowls and a very nice selection of high end mens shaving things.
The people who run it are friendly and speak some English. They’ll tell you how to care for your baskets. The bright ones need to be dampened once in a while. There’s a nice selection of baskets and the prices on those aren’t bad. The stock spills out onto the street on Korbergasse (basket street, actually) and you can also go up the narrow stairs to a room entirely filled with baskets of all shapes and sizes. It’s a good place.
A 2 minute walk from the Rathaus (or less), you’ll find it in the pedestrian area.