Picking somewhere nobody talks about usually means you're gonna have stories none of your friends can match when you get back. The touristy spots everyone floods are nice but they're all the same experience with crowds and overpriced everything, whereas going somewhere less traveled gives you actual adventure instead of just another photo op. Having your own vehicle changes the whole game because you're not stuck following some tour group's schedule or missing hidden spots that guides never mention. You can look at options to rent a car in Kyrgyzstan here:
https://getrentacar.com/en-US/kyrgyzstan . Tons of listings from people renting out their vehicles and you grab one that handles mountain roads well, set your own route, stop wherever looks interesting, and turn that random map poke into a trip you'll actually remember.