Katherine is spot on 300km from darwin (if memory stands to serve). It's a fair drive, but you have nitmiluk national park with Katherine Gorge and Edith falls nearby, a nice day trip and swim if you head out that way, with camping and basic facilities at Edith falls or hotels/motels in Katherine if it's a bit too warm during the build up season. Highly recommend Edith falls and Katherine Gorge.