Over the last 6 years of going to Gove for work we've identified a couple of reliable spots but all require boat access. Luckily, Gove/Nhulumbuy has a few sportfishing charters or you could buddy up with a local - just about everyone there has a boat of some description.
North of Bremer Island there's numerous pinnacles holding Big GT's as well as huge Macks, Barracoutta and good sized Northern Bluefin tuna. All will take a popper - you may or may not get it back
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South of Cape Arnhem again has numerous pinnacles and work well when the tidal flow is strong - we've been almost scared to put a lure in the water down this way some of the fish are that big.
Good jigging territory here if you wanted a feed of Reddies.
West of Melville bay are the Bromby Island Group, followed by the Wessels Group. The reefy flats adjoining the island passes always have large to unstopable GT's around - actually they can be a bit of a pain it you're targeting Coral Trout, either by beating the trout to the lure or by actually eating the trout you've hooked.
Big cod can also be a problem. You can camp on the Brombey group just remember to get a permit from the NLC.
regards,
sheds.