S.R.
Hi and welcome to the area! I am from NJ too :)
My favorite beaches are Palm Beach and MacArthur Park which is on Singer Island. Palm Beach is nice for families, there is plenty of free parking along the side sreets and there are lifeguards. MacArthur Park is more of a tranquil setting. You have to pay to get in ($3 I think) then you walk or take a shuttle across a wooden bridge over the intracoastal to get to the secluded beach. It's really beautiful there. Lots of shells to collect if you are in to that. They also have a small nature center which is nice for the kids. There are no lifeguards on the beach though, so I prefer to go there to relax but not go in the water.
Other things we like to do are The Palm Beach Zoo and Clematis by night in downtown West Palm Beach. There are also a lot of nice restaurants and shops to go to on PGA. Lastly, there is a place I've been wanting to take my son in Palm Beach Gardens called A Latte Fun. It's an indoor playground with foam pits, slides, trampolines, toys, etc for the kids and a coffee shop for the adults. It's gotten some great reviews.
How old are your kids? My son and I are always looking to make new friends for playdates. If you are interested in meeting up you can email me at ____@____.com.