I've never been to the Moose Hillock in New York yet, But have been to the one in New Hampshire a bunch of times. Large private wooded sites and I believe this year they started doing weekend themes and all day activities to keep the kids busy. Great pirate ship / Caribbean style pool.
There are a ton of attractions in White Mountains region. Moose Hillock is on the west side of the mountain closer to Lincoln (Hobo Railroad, Whales Tale Water Park, The Flume Gorge, Clarks Trading Post, Lost River Gorge) which is a nice area of little shops and restaurants, then you can travel down the Kancamangus Highway for some incredible mountain views into Conway where you have more attractions (Story Land, Conway Scenic Railroad, Mount Washington Auto Road)