This list does not include Kaufhof, Karstadt, Globus, Herties etc. The department stores normally do accept VISA and MC, but rarely the other credit cards. Except where noted - do NOT expect that the small shops will accept credit cards. Some may take the EC card or Eurochecks. Few, if any are going to be interested in Traveler's checks.
Cash is the way to go with all of the small stores.
ATMs are common in all towns. If you are looking to purchase TAX FREE, you have to get the paperwork at the time of purchase. Doing the paperwork is at the discretion of the shop keeper. Most of the stores, but not all, also carry extensive needlework supplies. Hours conform to Germany store closing laws.