Hi, I did a 4WD/camping trip in this July year. Wasn't really the right time of year for fishing, but a had a bit of a flick, I didn't get anything but my boyfriend caught a 87cm barra at the Roper river near Mataranka (silver lure). Did a few nights bush camping at 4 mile hole, Kakadu and caught a little barra, but there were big (90cm+) frames on the bank - think we really needed a boat. Beautiful spot though, and saw lots of crocs etc. Be wary though, fishing regulations throughout Kakadu.
Apparently Cahill's crossing (near Jabiru) is the best barra fishing in Kakadu, although had no luck there myself - it was really, really low tide and I don't think that helped. Ubirr rock near there is worth checking out as well.
The Cooinda lodge has accommodation and bistro, pool etc. It's also close to Maguk/Barramundi gorge, which is nice for a swim (no fishing though). Jabiru has the same thing, I think there's another resort on the South Alligator, perhaps just look up Aurora resorts on the web?
Hope that helps!