Allow the cathedral quarter some attention
Arriving at the main station brings you close to the cathedral almost immediately. That makes it a useful landmark, but not necessarily the right place for an indoor visit while carrying a suitcase. Take luggage to your accommodation or suitable storage first. You can then appreciate the interior, outside views and surrounding streets separately instead of trying to do everything while still arriving.
Worship and sightseeing have different requirements. Check visitor access directly with the cathedral and keep that part of the day flexible. Climbing a tower is also a separate decision: it uses time and energy that you may want later beside the Rhine. It is not a requirement for a worthwhile first encounter with the building.
Make an old-town and river loop
From the cathedral quarter, continue into the old town around Alter Markt, the town hall and the lanes leading towards the river. Many historical buildings were reconstructed. Considering their façades as part of Cologne's history and rebuilding reveals more than imagining an entirely unchanged medieval setting.
Give the Rhine one continuous stretch rather than making repeated detours to it between other activities. After the old-town walk, you might follow the waterfront and decide at a chosen bridge whether there is time to cross. The opposite bank changes your view of the cathedral and centre, but also lengthens the return journey. If a train departure is approaching, a shorter riverside section is the more sensible choice.
Give the second day a focus
Museum Ludwig stands beside the cathedral and suits an interest in modern art. The Wallraf-Richartz Museum offers a different collection focus. Read their descriptions and choose according to your interests rather than visiting whichever building appears first. One substantial museum between meals and departure is more realistic than attempting two complete collections.
Friends do not have to share every activity. For a museum interval, you can divide into smaller groups and arrange a clear meeting point outside, with some flexibility in the time. Anyone staying outdoors can plan a short route of their own rather than spending the whole visit waiting on a bench.
Accommodation decisions should consider the evening surroundings as well as distance from the main station. A location in a nightlife area can be convenient for restaurants, but a quiet room position is worth asking about specifically. Before leaving, save the route from your accommodation to the actual departure station: Köln Hauptbahnhof and Köln Messe/Deutz are different stations, and assuming the wrong one creates an avoidable final rush.
