Fogg Dam is also a nice visit, and is only an hour or so outside of Darwin. You typically get to see 90% of what's in the Territory Wildlife Park for free.
If you are doing a tour of Kakadu spend more than a day as Kakadu is huge. Litchfield should be a couple of days as well. Katherine River gorge is beautiful and so is Edith Falls. Try and camp near the gorge at the campground, because there usually a lot of wallabies around in the early morning. I don't know if trying to cram all 3 into one trip is worth it, instead of really exploring Kakadu and Litchfield. It really depends on how long you're in the area for.
In Darwin, a dinner on the wharf is nice and the food is pretty good. Mitchell street is good for a drink at one of the pubs. The noodle house on Mitchell, and Moorish Cafe on Knuckey are nice places to eat in the downtown area. If you can, try to get out to fannie bay at the trailer boat club or sailing club (next door), because they offer nice views of the sunset along with dinner. The #4 bus takes you there or a taxi. Mindil Beach market also offers nice views of the sunset on Thurs and Sun, with a number of food stalls (the food itself is hit or miss, but the woodfire pizza is pretty good). The NT Museum and Art Gallery is worth a visit if only for the cyclone tracy exhibit.
As you've probably already heard, spend most of your trip at one of the parks rather than in Darwin itself. about 8 years ago