Actually this was the first time we rented bikes in a large city and for Copenhagen it was perfect! The whole city is adapted for it, lots of bike paths and plenty of space in the traffic. Another important thing, the drivers were careful.
After three day there we had probably seen most of the 'tourist' parts. Our favourite places were along the harbour with all the nice places to spend days just watching time pass by, especially Christianshavn with its relaxing and energizing atmosphere. Not to forget all the parks that are amazing and plenty.
Another thing of importance to us is the food :) which was great. Sea food and of course I finally got to try out open-faced sandwiches (smörrebröd) which were a work of art. Recommend strongly restaurants Aamanns and Musling.
Copenhagen is for sure one of the best cities in Europe.