I'd say that if it's nice weather, head to Bonn. Enjpy the Old Town, the University and adjoining gardens and have a leisurely lunch in the city. Very pictoresque.

Dusseldorf is a good choice if it's raining or colder. On the Konigsallee and the nearby department stores all the shopping needs one could ever have can be fulfilled. Food choice is well above Bonn and some of it is truly excellent. It has a more big city feeling and is mostly about business but shopping and eating are well catered for.

Another option would be Koblenz about an hour by train from Cologne, one of the most scenic German cities.