Cologne is an interesting City - and a fun place to sit around and drink a kolsche or 7. But you can look up what to do on google. And eat pig ...loads and loads of pig
Maarsticht is not far away and very pretty
The Eifel region is stunningly beautiful and on the german/ belgiun border. There is also the weirdness of the Hohes Venn just over the border
Monschau is worth a visit and a stop - and so is the lake in the Eifel - and I can't remember it's name !!
Konigswinter, just south of Bonn
The Romantic Rhine - but the Mosel Vally is better. Trier is a pretty place to stay at the end of the Mosel valley, with some interesting roman bits in it
Fantasialand theme park in Bruhl - just outside of Cologne
Further south Heidelburg is well worth the trip
If you want grim but thought provoking - Bergen Belsen nr Celle
Bremen is nice, Hamburg is a great city ....