Is the best way to see the city. Bikes are respected all around the town and copenhageners themselves uses it frequently.
There's a lot of places to rent a bike, even you can get one on the back of Copenhagen Central Station (Københavns Hovedbanegård, København H)
It is closed on Saturday afternoons and on Sunday it is only open between 12-13h.
Here is another great way of getting a bike. CPH bike rental in Turesensgade. It's five minuttes walk from Noerreport Station. It's a development project about sending bikes to Africa. Everything is financed through the bike rental. Their prices start at 60 dkr/day.
For more information see: www.cph-bike-rental.dk