In my opinion, Kakadu National Park is one of Australia's most impressive sites. Home to ancient culture, gorgeous natural scenery, and a colossal variety of plants and animals, there's a lot to love about Kakadu. We visited the park over three days in June 2016, which gives you ample time to explore the various areas.
To reach Kakadu, your best option is to drive in from Darwin - a roughly 2 hour, 150km drive. It's best to go during dry season (May-October) as this is also the coolest time of year. Wet season from November-April is hotter, stickier and of course wetter: many roads in Kakadu will be flooded and impassable.
Aboriginal Australians have lived in Kakadu for around 50,000 years, and it's the oldest continuous culture on earth. Locals today can look at ancient rock paintings and understand the stories as if they were painted yesterday. The best rock art in Kakadu is found at both Ubirr and Burrunguy (formerly Nourlangie Rock), where you'll find a lot of interesting stuff: animals, humans, and spiritual art like the Rainbow Serpent who created the world during the Dreamtime. Ubirr Rock is also a mesmerising place for sunset.
For bird-watching, Yellow Waters Billabong near Cooinda is the best place. A great option here is to grab a sunrise or sunset boat tour - we managed to do both and preferred the sunrise tour as we saw more, though this is probably dependent on luck and the skill of your boat guide. There's over 300 species of birds in Kakadu, and something like a third of all bird species in Australia either live or pass through here.
Despite the crocodile threat, Kakadu is also a great place for swimming. Make sure you check out Jim Jim, Maguk, Gunlom, and Twin Falls. All of these can be swam at, but if there are closures due to crocodiles don't risk it. Also, some of these will need guided tours as they're accessible only via 4WD tracks. Don't attempt to take your rental Corolla down a 4WD track, please!
And finally, if you're intrigued by crocodiles (and who isn't!), make sure you stop at one of the Jumping Croc cruises on the Adelaide River, about halfway between Darwin and Kakadu. It's outside the World Heritage area, but seeing enormous crocs surge out of the water to grab dangling hunks of meat is quite a spectacle!