Public transportation
The most popular transportation in Copenhagen is the bicycle. There are bike lanes on all the city's thoroughfares. Perhaps you'll decide to join the locals and opt for this mode of transportation?
An alternative mode of transportation
You can rent a bike, for example, on this website or here, or at one of the rental shops in town. You can also borrow a city bike from a special rental desk: just drop a 20 DKK coin into the slot by the handlebars and get it back when you return the vehicle.