Cumberland Falls is one of the few places in the world to see a moonbow, a rainbow that forms in the water's mist at night. The park website has dates for when the phenomenon occurs each month. A one-mile round-trip trail takes you to the falls, a 125ft-wide curtain of water that's pretty dramatic anytime.
The park has a seasonal campground (tent sites $17 to $24, RV sites $26 to $37; closed mid-November through mid-March), as well as rooms at DuPont Lodge (from $85).