The Kaçkar Mountains, located in eastern Turkey just south of the Black Sea, are a mountaineer's dream. Think innumerable alpine heights (including high point Kackar Dagi - 3,937 meters/12,917 feet) interspersed with glacial lakes and old-stone villages. Think ravines blooming with wildflowers, typical rolling highlands called yayla, and Turkey's most challenging whitewater rivers: the Barhal and torrential Corah. Think the perfect adventure circumstances without the worry that you'll be surrounded by doddering pensioners.
The most popular destinations from which to access the Kaçkar Mountains may have to be Ayder, Yusufeli, and the far less touristy Olgunlar to the east. These more central towns may be reached via public transport from the main hub of the region in Trabzon. Once in the mountains, there are a plethora of trails worth your sweat, although you'll need ice climbing equipment if you plan to summit these alpine peaks between September and June. Otherwise, there are still a ton of moderately challenging hikes that don't consist of forays with frostbite and dizzying heights for the woefully unprepared.
Once in Ayder by Dolmush (a shared taxi that runs planned routes), you'll have the opportunity to head up into the highlands of Yukarı Kavron and the summit of Kackar itself beyond. Much closer to town is the gorgeous Gelin Tulu waterfall, spilling down a fold in the mountainside and inviting travelers for a closer look. After your day(s) of hiking, a revitalizing dip in the local hamam hot springs back in town really works wonders.
Yusufeli is a great take-off point for the level IV and V rapids of the Coruh; it'll be no problem finding a tour provider there who will whisk you into these roaring rapids. You'll also have no problem finding a trek to suit you, especially if you're looking to track through these valleys in pursuit of ancient Georgian castles or churches wreathed in wilderness.
For more information, we've thrown together links that include personal experiences, thrill-seeking footage, and insightful write-ups on Ayder and Yusufeli.