Hike one of the surface trails at Mammoth Cave National Park to see a spring in which groundwater emerges out of a cave. This trail also brings you by the Historic Entrance to Mammoth Cave and has views of the Green River.
Starting from the Mammoth Cave Visitor's Center, take the "Historic Entrance" trail that descends down the hill between the Visitor's Center and the Mammoth Cave Hotel. After 0.2 miles you will reach the historic entrance of Mammoth Cave on your right side. You cannot go in the cave without a guided tour, but you can walk down and look at the entrance.
The trail splits into two trails at the historic entrance. Take the wider trail on the left side which has a sign stating the River Styx Spring Trail. You will descend for 0.4 miles. When you level out near the Green River, take the boardwalk to your left to view the River Styx Spring, which is where groundwater is discharging from Mammoth Cave to the Green River.
There is also a small area where you can view the Green River. When finished, walk back the way you came up the hill to the Visitor's Center to complete this short and easy hike.