MSPeconomist

I'd compromise and go to Bonn, which is a very pleasant, interesting, and convenient small city. You can easily take the train or streetcar to Koln to see the cathedral, which is the main attraction (plus a few other old churches and parts of the old town wall and of course a downtown pedestrian shopping zone) or go in the other direction to see the castles between Koblenz and Mainz.

Assuming that you arrive in Bonn by train, be careful about which train station you use. The older main (Hbf = hauptbahnhof) station is in the very center of Bonn and is the hub for local public transportation. The new station for the fast trains is across the river and almost at the edge of the suburban area. It's an expensive taxi ride to the center and you would probably want to use a taxi to get to your hotel, even if it's in the very center (versus many hotels being easily walkable from the Bonn Hbf.) IIRC the long distance trains along the Rhein (north-south trunk lines) seem to alternate between the two stations, with hourly direct service from FRA, and you *might* need to have a ticket for the correct station. [The last time I did this, there was also an issue with the train station at Mainz which resulted in some trains being diverted to a suburban station on the other side of the river, but that seemed to be a temporary construction/track work thing, so it should be easy to go to the Mainz Hbf to be in the interesting center of that small city.]