I have just returned from Darwin... Mindil beach is about 2 mins from the main strip in Darwin and every day I was there, a nice cross on shore breeze was blowing about 15-20knots.
Unfortunately there are killer jelly fish in the water so you need a full body "stinger suit" and yes - watch out for crocodiles...
There aren't that many crocs at Mindil, but it is a possibility... The beach itself is an ideal kiting location, 30 - 50 metres wide, then some easy trees and shrubs that line the beach.
Call the Darwin Met Service, i don't know the number...If you want nice flat water kiting - it certainly has potential.
Don't say I didn't warn you about the stingers and corcs, though