You could look into the Tabletop Track in Litchfield for a multi-day walk - there are a lot of shorter walks in Litchfield, most of which accessible via 2wd. As well, the swimming here is excellent as for the most part you do not have to worry too much as it is mostly up on the escarpment.
There are also plenty of walks that start at Katherine Gorge other than the Jatbula as well that you should check out. Another option is to hire a canoe and take it up the gorge for something a little different (did this many years ago).
https://nt.gov.au/leisure/parks-reserve ... ional-parkAs well, if you get the chance head south of Katherine to Mataranka - Bitter Springs is a favourite spot with camping nearby. Mataranka Thermal Springs is not as nice but worth a look. If you do not get time, while in Katherine, check out Katherine Hot Springs just south of town.