CPH is in the fase of building up the "new" CPH, and in this process, it is said that they will include a "spotter"-area in terminal 2, but this has yet to be seen.
All in all, CPH has only a few good spotting places around its perimeter.
About halfways down RWY 22R theres is a place called "Flyvergrillen", heres there is a mount from where you can get an overview of practical the whole length of RWY's 22R/04L and 04R/22L. This is the most used place, about 20 mins walk from the main terminal.
At the end of RWY 22R ("St. Magleby") and 04R ("Kystvejen") you are able to get a pretty good veiw of the incoming flights. (Depending on the windconditions of course).
At the start of 04R you will be close to the treshold, and be able to get a few good shots.
RWY 30/12 is almost impossible to get a good look at, but they use it seldom, so it doesn't really matter.
At "Kystvejen" you do also have the opprtunity to get a small look at the cargo-apron.
At all places, except from "Flyvergrillen" you are alsmost certain to run int airport-security guards, but I guess that's a problem all spotters are only to familiar with!
My best advice would be to go to "Flyvergrillen".
If you like more specific guidelines, then send me a mail, and I'll try to send you some maps.
Best regards Dan