You could do a walk along the water - around where the aquarium is and north towards the fort.

I have never walked around outside the airport but my google maps says 20 minutes (1,6 km) walking to the aquarium (Den blå planet) and gives the route :
Walk down Ellehammersvej until you reach the big roundabout, turn left and exit the roundabout at the next road Amager Strandvej.
Walk down Amager Strandvej for a while and turn right down Jacob Fortlingsvej.