If museums are on your list of things to see, you might want to browse the collections at Thier-Galerie in Dortmund City Centre. If you want to see more of the museums in Dortmund, you can easily walk to German Football Museum or Dortmunder U.
If you like haggling for the best price, you might want to head out to Dortmund Christmas Market in Dortmund City Centre and take in the atmosphere. Splash some more cash at Westenhellweg Street, Hansaplatz, and shoping and pedestrian area.