While getting a permit in requires a little work, the incredible waterfall into Neversink pit offers a view like no other.
Neversink Falls - Trip Details
Since the Neversink Preserve property was bought and established by the Southeastern Cave Conservancy in 1995, the SCC has been using a permitting process to control access to the preserve. Once you and your group is approved for a permit, you'll need to place it on your car when you're visiting. You'll get details on parking from SCC. If you're looking to pick up the skills required for a visit and don't have them yet, consider connecting with a local caving group. You can find a list of the ones in Alabama at caves.org.
You can request a permit from the SCCi on their site.
More Waterfalls around Neversink Preserve
Neversink Pit is closest to Stephen's Gap, another SCC property that requires a permit to visit. For less extreme waterfalls that are open to anyone, the hike to Lost Sink Falls is a fun one and Pisgah Gorge Falls is just across the river.