I don't fish Sandy Hook regularly, but I do surf fish down in Ocean County. I am sure someone else who fishes around there will chime in soon.
I would target fluke and bluefish. For fluke you can put bait out on a fluke rig with a pyramid sinker. Squid, spearing, killies and bunker will all work. You can also use a bucktail tipped with any of the above or gulp. I would tie on a teaser as well tipped with bait or gulp. For bluefish, chunked bunker will do the trick on a bluefish rig or a fish finder rig. I would keep some metal lures: Hopkins, Croc spoons, AVA's and some topwater poppers readily available in case a school goes by.
You can also target kingfish and croakers, but that might just be a waste of your time...unless you have a couple of setups available. Worms, clam or squid on hi-lo rigs work real well. I haven't heard too much talk of kingfish or croakers this year so and I am not positive if they see them up in the surf there at SH.
Either way have a great time and make sure you get to the beach very early or wait until later because the weekends have been full to capacity!
Good luck and enjoy!