My Mom has a little shack on LBI just outside of Beach Haven.
It seems very family friendly. There is no boardwalk though. But there is Fantasy Island and a bunch of other family themed things.
http://www.fantasyislandpark.com/
It is just north of Brigantine and takes me about an hour and ten minutes from the Ben Franklin to the Causeway (the bridge to the island) doing speed of traffic - close to the speed limit. There is a common misperception that LBI is up north somewhere but it is actually just a little south of Philly.
I love it - it is a very long skinny island - so it is usually just a couple blocks from the beach to the bay. It sits further out at sea than other islands so it is always very breezy. And the waves tend to be better than other islands. It just has a very cool laid back feel. At least the part I am used to. I am not sure about areas like Loveladies where everything is multimillion dollar sand castles.
http://www.longbeachisland.com/
http://en.wikipedia.org/wiki/Long_Beach_Island