Have you looked at any of the forums for suggestons so far? There is lots to, but what do you like ?
Our storms are nkt as bad as those on the east coast. We are used to rain up here. and usually there is lghtning etc. storms pass over quite quickly and then it cools and clears. Unless you get a low pressure ststem or monsoon comes, it wont rain all day.
it deosnt matter what the weather has been like ... :) it what it will do later is the question. Who knows. Check the BOM weather site for radar of rain and storm warnings.
You could do a day trip to Litchfield, nice and coo for swimming.
Kakadu would need two nights -one njght would be a rush given that its a three hour drive eacway and thendriving within the NP. Yes some things are closed, but they are dirt roads and unless you have a 4wd iyou cant access anyway. There is still plenty to do. But walking out there will be hot . Check out Bowali Visitors centre for whats open and get your access pass to Kakadu.
Dont swim at our beaches as there are stingers and crocs about.