Sandy Hook was an artillery testing range back from Revolutionary War days on up, you may be able to find some goodies laying on the bottom yet. Heading West you have the Navy pier, there is a lot of stuff scattered up to a mile away from someone dropping the wrong thing, resulting in a lot of ship pieces going sub-orbital. I'd be careful not to get too close to the pier nowdays though.
Lots of diving going on down South in the Belmar - Tom's River area.
Come winter when the boats are put away the Shark River inlet is a fun dive, though you have to catch it on the incoming tide (clearer water) & drift along hovering a few feet above the bottom. You can catch runs of breeding horseshoe crabs & eels where the bottom is almost paved with them.
Check the bridge abutments for bugs. Used to be a lot of flounder in there too.
Offshore in the warmer months you have the wrecks, check with the local shops to see which ones they're running to.
I went back for a visit a couple years ago & didn't recognize the place so I'm not up on current specifics.
Look around our various forums.
