E.R.
Long Beach Island, esp Beach Haven, has LOTS for family: amusement park and arcades, mini golfs, shopping villages, free concert in the park every wednesday, The Showplace Ice cream parlor, beaches and bays, lighthouse...
I grew up there and my parents own a shop in Bay Village (Beach Haven), called Personality, check them out!
You can rent your own house or stay at a bed and breakfast or hotel or condo on the beach. But renting your own house for a week would be ideal, invite other family members to join you and then you'll have built in babysitting! Lots of nightlife, too!