Renting a bike in Copenhagen is a great idea! As you know bikes are the most ecological way to go around the city. They are also very useful for your health! Below are some websites where you can find the cheapest bike rental in Copenhagen:
RentYourBikeHere.dk is a great, local company that offer you a possibility to order your bike online, before you even arrive in the city. They also provide guided bike tours, useful info on biking in Copenhagen and many more. Check out their website for more information!
Before you start your ride, be sure that you have lights on your bike! I’ve fond unique bike lights at CopenhagenParts.com. Small, local company that design and produce great bike parts. They also produce beautiful bike porters which can be useful during your stay in Copenhagen.