You might want to check out
www.urbanhound.com They list all the good dog runs in the city, including the private ones where they might charge a little fee. We have a park across the street where Archie goes everyday (although it says no dogs allowed, but really, who follows rules when it comes to their dogs?!) but he also goes to the dog run several times a week. I work downtown and would love to sneak Archie into Battery Park.