https://folkartmuseum.org/
Located in Manhattan the museum has an extensive collection but uses its visitor space primarily for special exhibits.

longislandmuseum.org Fabulous transportation collection and extensive holdings of William Sidney Mount

www.cshwhalingmuseum.org
An intimate museum with a lovely collection of scrimshaw. Great for kids.

www.oldbethpagevillagerestoration.org
A Long Island farming community of the 19th century. Really kid friendly. Summer old-time baseball games.