Why not spend it in Frankfurt? It is not that bad at all.

Wiesbaden is next for Frankfurt, easy reachable by public transportation (S-Bahn, several direct trains from Frankfurt Hauptbahnhof (Main Station). There is a small park called “Kurpark” and you could walk through the city. But as the shops are a closed, it could be a little bit boring on the one hand, on the other hand the city is not so crowded. If the weather it not that good (rain, snow, etc), I would not recommend it.

Cologne is an hour by high-speed-train (ICE) from Hauptbahnhof, but you should expect to pay app. 80.00 – 100.00 EUR for a round trip. In Cologne you can visit the cathedral (Kölner Dom) and walk through the city of Cologne and at river Rhine. The city of Cologne is next to the station and therefore easy to reach. Information about Cologne could be found on the Homepage of Köln Tourism. There are several museums, which you could visit if the weather condition are not so good. I recommend the Römisch-Germanisches-Museum, Museum Ludwig , Wallraf-Richartz Museum or Schokoladenmuseum, a museum about chocolate.

Düsseldorf is another twenty minutes by train from Cologne. It offers a nice Rhine front and is famour for its Altbier, but you should visit Düsseldorf in more warm weather. We have some museums and the homepage of Düsseldorf Tourism could be found here.

The best combination would be, as recommend a few posts earliers, to travel by train through Rhine Valley via Koblenz to Cologne in daylight, visit Cologne and return by High Speed to Frankfurt in the Afternoon.

Feel free to PM me if you have any questions