Honestly, the only difference between LBI beaches is how many people are on them. From Surf City south to Beach Haven, they'll be slightly more crowded. The northern and very southern ends of the island are less crowded; some may not have lifeguards. Oh, and the dunes are much wider up near Barnegat Light. Only one or two public bathrooms on the bay beaches, no amenities, no boardwalks other than Fantasy Island which is not on the beach. You're probably best off choosing whichever beach is closest to where you're staying so you can make trips back to the house/hotel for the bathroom, etc.
Unless you go off the island, there isn't a ton to do other than play on the beach or in the water. You can climb the lighthouse; that will take all of 30 minutes--probably as long as the drive up there if you're staying at the southern end of the island. Or you could rent kayaks/boat/jet skis--several places on the bay side have rentals--or go fishing.
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