We stayed at Discovery Parks Katherine and recommend it! It’s a bit outside of town and we felt very safe. It was very nice and quiet, plus a short drive from Nitmiluk Gorge, with cabins and caravan sites.
Check current availability and prices here.
Here are more suggestions:
Riverview Tourist Village: Best for Katherine Hot Springs, with the pools accessible directly from the caravan park. It has cabins, powered and unpowered sites, a pool and pet-friendly options.
Nitmiluk Campground: Best if you want to stay inside the National Park without breaking the bank. It has powered and unpowered sites, plus a swimming pool.
Cicada Lodge: The fancy option inside Nitmiluk National Park, with a pool and restaurant. It’s around a 15-min walk from the jetty.