Ask for Marmorvej 51 - UN City. It will cost around DKK 350 (USD 58).
At the airport, ask for a three-zone train ticket (it will cost DKK 34, that is USD 6) and check that "Nordhavn Station" is announced on the train departure screen. The "S-tog" Trains from the lines A, B, C and E stops at Nordhavn Station as well.
The walking distance from the station to UN City/FN Byen is approximately 900m (as indicated by the red line on the area map).