I did the Lichfield and Kakadu tours - fantastic!! Lichfield tour is better than Kakadu tour IMHO. I didn't get to see Kathering Gorge so can't comment.
Also did a small plane 1 hour ride. You can't hear a bloody thing (recorded info that's coming through a set of headphones) over the noise of the engine but the view is fantastic and you'll see some views of waterfalls that you just can't see from the ground. You get to really appreciate the sheer size of the place from up there.
You must do a croc tour, but make sure you're in one of the bigger boats. One of the highlights of our croc tour was getting to see wild whistling kites - (quite a large eagle like looking bird) catching food on the wing that was thrown up in the air. There were 100's of them swooping and diving for the food - it was absoutely awesome. This feature wasn't advertised as part of the tour as it's not exactly part it - it's just evolved over time and the birds are now used to the feed.
The markets are great especially if you like Asian food, tropical fruit drinks and 'Bali' type clothes.
I have a friend up there who took me to all the historical places in the city and knew the history of it all - don't know if there's a tour for that or if you're into it (Government buildings etc).
Go to Aquascene at Doctors Gully to hand feed wild fish that come in certain times each day.
Visit the jail, museum & art gallery.
The oil storage tunnels is a bit of an unusual tourist attraction (
http://www.darwintours.com.au/tours/ww2tunnels.html)
View a sunset from Mindle Beach or Fannie Bay
Have a beer at the open air bar on the beach near the boating club
There's a nice indoor rock climbing place if you're into that - made from one of the oil tanks to do with the oil tunnels left over from WWII mentioned above.
I found the Pearl Diving Museum interesting.
Can't remember the name of the place but they've done up an old bit of marina and there's a nice walk and eateries there now.
Catch a movie at the outdoor cinema - deckchairs provided.
I went Easter 2006 and the water was still quite high up. One boat tour I went on was of the marshes/swamps/lakes (can't think what it's called now). Every time you turned a bend it was a different scene. Lots of wildlife, water lilies etc. So peaceful & beautiful and a must see.
Darwin city is basically just 1 street - everything to see and do is ex city. If you are in the city the cheapest and 'best' eateries are near the backpackers place. You book the tours near there too.
Have a great time.
Olly