When visiting Copenhagen you absolutely must take a ride with the new metro. The Danish metro is from 2002 and was made by Italian AnsaldoBreda. Even though it seems to me that the Danes are always complaining about it, I find it fabulous. You get around really long distances in no time, the design is fantastic and the best of it: The metro is driverless, which means that you can sit in the front and look ahead while driving.
The metro is also the most easy way to get to and from Copenhagen Airport. It takes around 20 minutes to the center and trains depart constantly.
So do yourself a favor. Take the metro when in Copenhagen- just for the fun of it.