Nope! When I took my kids there, I parked on a street outside of a school a couple blocks away. Zero parking at the beach. That being said, it's well worth the visit. It's a beach with a playground.
No, there is a little bit of a dead end street but it isn't meant for parking. There is a high rise that has drive way access right near there. The city has been known to ticket cars parked there.
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