Prielbrusye National ParkThis beautiful waterfall is located just a short hiking distance from the village of Terskol, Caucausus. The hike took us about 2.5 hrs up, and less time down (I did frequent stops to take photos of the local flora, which was amazing in July). There are beautiful views of basalt rocks along the route, Mt. Donguzorun, Cheget, and you can continue higher up to the observatory, which gives you wonderful views of the Baksan Valley and Elbrus.
You do not require a permit for this hike. All walks near the Georgian border require a permit.