There are some pretty good hang-outs around there. Be careful around the Sandy Hook bridge. REAL strong currents going through there. I was inches away from getting killed there years ago in a friend's POS 15' Tri Hull.
I'll second that about the currents at Sandy Hook. Last time I fished out of there on a borrowed Boston Whaler, it was easy to forget how that current rips at the bridge and around the hook by the CG station. But, around the bridge pilings WAS the best fishing... a few (more) scratches just added character to the boat! My kids worked a bluefish/rockfish blitz just inshore of the bridge supports for about an hour. But if we got more than a boatlength away, nothing. Trying to hold position in that current was a test!
It would be a worthwhile weekend trip. there is good sightseeing in the form of massive multi-million dollar homes along the river. There are places to dock and dine in Red Bank and the Highlands. You can easily take a cruise around Staten Island or up to the Statue of Liberty. There is good place to raft off and party just off Hartshorne Woods Park referred to as "party cove" if I recall correctly. There are even quite a few good free municipal launch ramps in the area if you were going to be trailering in. the only thing I can tell is girls phone numbers in that area.........anymore