The NRW-Express needs 1.5 hours for the 100 k to Cologne, but it's cheap for students: only € 3 - 6 (from Cologne/ from Dortmund) with our VRR semester ticket VRR (Rhine Ruhr Public Transport Network).
Cities between Dortmund and Cologne:
Bochum, Essen, Mülheim, Duisburg, Düsseldorf, Leverkusen...