Absolutely Cologne. My girlfriend lived there and while we lived in Germany, I visited her about every 2nd week for months - never got bored with the city. The local beer Kölsch is really good and there are tons of breweries. Be sure to check out the parks on the east side of the Rhine and tour some of the promenade on the west side south of the main station.

Also, the chocolate museum is a hit most people like - last time I was there they had a chocolate fountain where you can dip cookies in. And it's real chocolate not the stuff you get in the US.

I do not know too much about the gay scene but Cologne does have a reputation in Germany to be very gayfriendly city with a big community. They even have gay parades at least once a year.

And if you're in the area, Bonn with is maybe 15mins south is also worth a visit. It was the seat of the German government from after the war until reunification and has a nice residence castle. In the southeast of Bonn are a few mountain ("Siebengebirge") where you can take a railway up (or hike) to enjoy a great view of the area.

Have a great time!