Kakadu is huge, so where you stay matters.
Cooinda is best for the Yellow Water Cruise and the southern spots, while Jabiru is better for Ubirr, Burrungkuy / Nourlangie and the northern side.
Here are some suggestions:
Cooinda Lodge and Campground: Best all-round base for Yellow Water Cruise, with rooms, camping and caravan sites
Mercure Kakadu Crocodile Hotel: Hotel option in Jabiru, good for exploring the northern side of the park
National Park campgrounds like Karnamarr (near Jim Jim Falls) or Maguk (near Barramundi Gorge). Both are 4WD only and for self-sufficient campers! Book your site online.