As far as i know ,legally you aren't allowed to bbq in brooklyn except in prospect park. I've seen ppl in all the parks bbq anyway but just letting you know.
On 79th and shore there is a basketball court and a concrete area where there aren't any trees near. But there aren't any BBQ grills, need to bring your own. I believe on 83rd and shore there is another area to BBQ as well.
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