Various brands within the old Quality Inn chain (called Choice Hotels now IIRC) seem well represented in Copenhagen. If you have some of their points, this could provide an option.

If you can find something within your price range, my instinct would be to try to stay between the train station (assuming this is the transportation you'll use to/from the airport) and the center, so that both are walkable.

Depending on your age, you might enjoy dinner and drinks at some small places located near various parts of the university that are basically student hangouts.