Here's my recommendations for visiting Copenhagen.
Copenhagen is a really nice city to explore, it's fairly small in size and therefore easy to get around with busses, metro and trains. Bikes are also available everywhere for rent, but tourists renting bikes and not knowing how to engage in traffic is quite annoying and dangerous for us bike loving danes.
The canal tours are actually quite nice, and if you have time to go and are interested in the the history of Copenhagen, I'm sure you would enjoy.
Don't get too caught up in fairytales about vikings and little mermaids though, go explore different areas of the city other than the inner city. Nørrebro is filled with niche eateries, bakeries, coffeeshops, bars and people from all walks of life. Frederiksberg is the rich, posh and expensive area. Amager used to be farming lands for Copenhagen, today it's filled with tall appartement buildings and Amager Strandpark is worth a visit if you like bathing.
Studiestræde is the main gay street in Copenhagen with a variety of bars/pups catering to different experiences. Just go there and have fun, but good nights usually means you end up at Jailhouse to chat and get drunk, before going to Nevermind to dance until morning.
If you are into techno Den Anden Side is the place to go with darkroom and maybe to an extend a dress code - you should look like you're there to party.
My favourite cruising spot is Frederiksberg Svømmehal in the luxury changing rooms that's 16+. There's a big steamroom and sauna. Most action happens in the steamroom, when the vibe is right. A huge recommendation, the baths are just the hottest place to check guys out.
SATS in Adelgade is a gym where alot of cruising goes around in the baths and the sauna. It can get very raunchy I've heard from my boyfriend.
Amager Fælled is a big nature area in southern copenhagen. Its accessible by metro and is a commen place to cruise in spring and summer. Never been myself, but heard a lot of good things about it from friends. Whenever the suns out, buns are out and things happen out in the bushes as soon as you lock eyes with a hottie on the gravelpath. The cruising happens in some areas and I know you can search and find articles and maps to explain more.
I myself plan to go explore this upcoming season once the weather is stable.
Ørstedsparken is the most traditional cruising spot, the park is not locked during the night, so men have been going there for hundreds of years (I think at least 200y). Cruising happens at night and often by the toilets. I haven't been myself.
A small disclaimer when interacting with Danes. In public danes come off as standoffish, because once we are outside we are usually very oriented towards what ever we are doing And not interested in being bothered. It's not normal to ask someone you don't know well "how are you?", it is viewed as a private question, not as courtesy. It can seem as if we are hard to get to know, but in reality we are more interested in direct conversations, instead of awkward courtesies. So stay centered on yourself, and don't get thrown off by our cold demeanor. We are softies on the inside, once you get invited into our homes we are warm and more relaxed in hygge vibes.
Hope this helps! Enjoy Copenhagen!