Can my kids play in the playground at UES asphalt green, or do we need to purchase a membership/day pass in order to enter playground?

Its open to public thanks.

Are you referring to the small park at the 90th street entrance? If so, I believe that is a public park.

Some times of the day, like early morning or sometimes during the weekend it is open to public. Otherwise you need membership. You can find the open access schedule on their website I guess or somewhere on internet.