I don’t live there but great idea, their stadium and its atmosphere is legendary. Dortmund as a city isn’t pretty and not really a tourist destination. It’s a former steel workers and coal miners town. Same goes for Essen (I have family there). Unless that’s exactly the type of stuff you want to see then you might want to visit the Zeche Zollverein in Essen.
Düsseldorf and Cologne on the other hand have lots to offer (tourist attractions, culture, history, entertainment, night life). Both are about a 1 hour drive or train ride from Dortmund. The entire NRW region is pretty well connected (one might argue it’s one big city). Roads and trains will be packed on game day though I imagine.