You have to absolutely have Allegany State Park on that list. It doesn't have the spectacular scenery like Letchworth or Watkins Glen, but it provides a wonderful outdoor experience for visitors. It is one of the largest state parks, if not the largest, in the nation. It has hundreds of cabins, ranging from non-electrified primitives to posh ones with indoor bathrooms, handicapped accessible, and providing linens and utensils. There are hundreds of campsites for tent and trailer/RV camping as well. There are also group camps that can be rented for family reunions and the like as well as a few camps with horse facilities.
Recreational opportunities include hiking (miles of trails of varying difficulties), cross country skiing, hunting, bicycling, etc. There are two large lakes (Red House and Quaker) for swimming, kayaking, fishing, etc as well as the smaller Science Lake for fishing. There are nature programs for children and adults. There are various sights within the park itself, my favorite being Thunder Rocks, which are these huge bedrock formations that were exposed by the original Appalachian uplift, and then worn down over the eons into what's left.
Allegany: Red House area
If you're going for scenics, why was the Niagara Falls State Park not on the list?
People come from all over the world to see Niagara Falls! Oh, yeah, and it's the oldest state park in the US!