There are over 3,000 individual waterfalls in New York State. I have been to a couple hundred.
High Falls, located in Chateaugay, is one of the more interesting of the region. It's located near a family campground, so you have to check in to the camp in order to see it.
You may know of other "High Falls" from your region. There are dozens in NY, just like Buttermilk Falls, Lower Falls, etc. All are very unique from one another. I think that is what makes visiting the different regions of NY so great. Rock formations vary from bedrock, to limestone, shale, fossil bearing, and everything in between.
Next time you're driving through the state, try to jump off the main highways onto the original "interstates" (Rt 5 and Rt 20) to gain a better picture of just how beautiful the state really is.