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I had a great vacation on Bald Head Island....an island off the coast of Wilmington NC...you get there by ferry and there are no cars on the island. You get around by golf cart. We went towards the end of August, which, at that time was not "peak" season...still high season...just not peak. I think that's because many schools start in August in that area. Very nice place, no cars is great, you can rent bikes and a nice beach. Many rental homes were available (we did a two family vacation). At the time (nearly 10 years ago), it was still somewhat undeveloped, so there wasn't a tremendous amount of shopping and a moderate amount of restaurants. Was a really nice vacation. Good luck.

Try looking into the Wildwood Crest NJ area. It is great for families! Has a beautiful beach. A great boardwalk full of amusements for any age group.