Long ago, Cologne had Saturn, the biggest record store on the continent (only beaten by something in London and something in New York). Alas, nobody buys records any more.
Sorry, haven't lived there in several decades. You said you did most museums already. Did you get to the Museum für asiatische Kunst? Quite nice, and not one of the usual tourist traps. Shopping for gifts: Get some "cologne" a.k.a. Kolnischwasser, at Glockengasse 4711. Drive to Aachen (45 minutes), and visit cathedral (including the place where Charlemagne was crowned 1200 years ago), and city hall. Aachen is also a university town, so if you go have a beer near Templergraben or Pontstrasse, you'll find lots of young technical people. Drive to Essen, about an hour, and visit the "Zeche Zollverein" museum of a coal mine. If you can get a ticket, drive to Schalke (another hour), and go to a Schalke 04 soccer game (make sure to NOT wear logos from other soccer clubs there, if you value your life). For hiking, the open strip mine area between Aachen and Cologne is fascinating, both because it has been restored to nature reserves in some places, and also because strip mining is the most extreme way of terraforming. If the weather is nice, the Eiffel (the mountains area about an hour southwest) is very pretty; visit some of the Maar (deep volcanic lakes), and Burg Elzt. Drive along the Mosel river (you can make that into a trip with Eiffel and Elzt), and look at some of the castles. If you are into music, visit the Beethoven house in Bonn.
And don't forget to visit Dusseldorf. Yes, people in Cologne don't like that city (local rivalry), but the shopping on the Ko is unbeatable. And if you go to the Altstadt (old city, also known as the longest bar counter on the planet), you will find a place to have a beer with locals ... and on a Friday or Saturday night, you will find a few hundred places to have a dozen beers with a few ten thousand locals. There is nothing like Dusseldorf's Altstadt in Cologne. Just make sure to not drive back, if you value you driver's license.
