I'd +1 on Central Park, but walk up to the more northern parts, who cares about fucking Strawberry Fields. So what if you've already been, I've been to the park hundreds of times and it still amazes me.
Coney Island is cool too. So is Harlem, mostly from Marcus Garvey park and north on Lenox. Good food and coffee shops. I like Astoria but meh for visiting.