You find hundreds of free maps today and many are you able to download to your gps or smartphone.
When you are crossing or investigating Copenhagen you got a good cyclemap on kk.sites,itera.dk
On ibikecph.dk you are able to download an applikation that gives you directions in you smartphone.
dac.dk gives you tips on what to see today in Copemhagen. Also with a smartphone app.
Then you also got google maps that is useful if you are able to use your smartphone on the handlebar:
gpsies.com is useful for you who would like to make your own track and then download it to your gps.
Visitdenmark offers an app to your smartpgone with 26 different routes and campings near by. The app detects where you are at the moment with gps and then suggest different bikeroutes around Denmark with camping. You are able to download it for android on google play and for iPhone, iPads om app store
Denmark is actually one of europes best countries for bicycling and especially Copenhagen.
Creative commons made a quick review about the possibilities for using your bike in Copenhagen. Lot of positive voices. See more on
If you don't have your bike in the luggage then you are able to rent a bike from 5€ or 8$ on rentabikecopenhagen.dk