on the beach during the day in seaside you need a beach tag. Before and after you should be ok, i was not bothered. if you go down to IBSP in seaside you need to stop by the office for a free permit.
Island Beach State park - permit -very restricted on time of day etc.
Sandy Hook is Federal=Not Legal as far as I know. However, I saw a news article that said some kid had a great find there. Oops.
Almost all beaches you need a badge during the day. When the lifeguards are gone have at it- no fee- Badges run from $5-$20 per day
Some beaches they kick you off at night.
A lot of places parking is an issue. Of course you can usually find somewhere for a fee. Check the side streets a few blocks in for no meters if you are cheap like me, and don't mind walking.
Good Luck!
Some exceptions here and there but that is mostly what I have seen.