Everyone comes here for the longest known cave in the world, but visitors can also enjoy the beautiful hills and river valleys. The Mammoth Cave Visitor Center houses exhibits and is the ticketing and departure point for cave tours. Tickets are required to access the cave.
I recommend the Extended Historic Tour. It's a self-guided stroll that uses the historic entrance, although rangers are inside to answer questions. You'll cover about 2 miles and it'll take about 90 minutes. This is a combination of the Broadway and Mammoth Passage tour routes, so you'll see formations like the Rotunda, Methodist Church, and Giant's Coffin. You'll also see manmade relics such as the salt peter mining site and the old stone tuberculosis huts.
Above ground, there are tons of short trails near the Visitor Center, most of which are under a mile. The .3-mile Sunset Point Trail offers a beautiful view of the Green Fiver Valley. The 1-mile Cedar Sink Trail features awesome rock faces, a cave spring, and abundant wildflowers. There are also several short trails by the South Side area, as well as the Mammoth Cave Railroad Bike and Hike Trail.
The park also has backcountry horseback riding, fishing opportunities, and private kayak and canoe rental. For lodging, the Lodge at Mammoth Cave offers old cottages or modern rooms. The Mammoth Cave Campground is the closest offering, although there are two other campgrounds and backcountry camping available.