i live in Sweden and have just got back from Copenhagen, have been there quite a few times.
you must rent bikes, it is the only way to see the city. it’s also a city that doesn’t really have main attractions as such, but just cruising round and stopping at cafes and streets you like is the order of the day.
if you are interested in cycling infrastructure google the green wave Nörrebro and experience it yourself. its also a really cool area. Meat packing district is great for going out
Also Louisiana modern art museum outside Köpenham is such a beautiful building and a wonderful place to spend the day in the museum and grounds.
its distortion street festival at the start of june if you are there for that?