The Museum and Art Gallery of the Northern Territory has a fine collection, but what is its most popular attraction by far? That's right - a preserved saltwater crocodile called 'Sweetheart.'
Sweetheart, a 50 year-old male, was menacing boats on the Finnis River, so he was captured by rangers. They intended to give him to a croc farm for breeding. Sadly, during the capture, the drugged crocodile drowned and could not be resuscitated. His body was given to the museum.
If you can drag yourself away from Sweetheart, there's a fine natural history collection and plenty of indigenous art. You'll also get a good grounding in the Territory's history, including Cyclone Tracy (there's a room that simulates the cyclone) and visits by Indonesian sailors back in the day. The museum looks beyond the mainland to focus on Southeast Asian and Pacific culture.
The Museum and Art Gallery of the Northern Territory is located on Bullocky Point, on Darwin Harbour and is easily accessible by bus from the city center.