score:4
I spent a while in Central Asia in summer 2011.
While backpackers were few and far between, there were actually more cyclists than regular backpackers - seems to be a bottleneck point for the trans-Asia cycling groups, I did meet a lot of people doing hikes - in Tajikistan and Kyrgyzstan.
Tajikistan is basically a country on top of mountains. It's spectacular. Like nothing you've seen.
Kyrgyzstan has one of the highest alpine lakes in the world, and lots of mountains as well.
Between the two is the Pamir Highway, a spectacular plateau made famous by Marco Polo all those years ago when he was investigating trade routes along the Silk Road and exploring the region.
The road is ... spectacular and ... interesting...very interesting:
but the scenery is unforgettable.
I would suggest a trip that includes hikes around the Pamirs. I'm not a big hiker myself, but all those I met doing it just raved about it.
For some extra interest and photos I'd suggest checking out Trekking The Pamirs.
Hiking groups were either doing it themselves, or connecting up with others in Bishkek, Kyrgyzstan or more likely, Dushanbe or Khorog in Tajikistan.
You'll need an extra stamp on your Tajik visa for the Pamirs, but it's like $10 and you just ask for it, but you will need it before you enter. And you WILL get checked - checkpoints everywhere!
Upvote:2
I have two suggestions for you:
Damavand
picture from hikr.org
You could climb the highest mountain in Iran and in the whole middle east. It can be done in 4 days, but it shouldn't be any problem to find a tour to do it in 5 or more days. But be aware, the mountain is quite high (5671m) and you should be aware of altitude sickness. Here you can find a description and some pictures. The text is in German, but you will get a first impression of the mountain. As you can see, the mountain is very prominent, similar to the Kilimanjaro in Africa. Depending on the weather, you should be able to walk up to this mountain, even though there may be a couple of situations where you also have to use your hands.
Ala-Kol
picture from hikr.org
You could do a small trekking tour from Karakol to Altyn Arashan as described in this post. It is an easier tour than the first one, but on the other hand, the mountains are not that high. And it is probably also more complicated to organize, since the starting point is not the destination.
Generally, I would recommend to check out the tours reported at hikr.org. It is a platform where hikers from all over the world report their tours, describe and rate them. You will also find a lot of beautiful pictures that give you an impression of the area. Additionally, there is a convenient search function that allows you to search tours in specific regions (in your case e.g. the countries in Central Asia) and also limit the search results to a lot of specific parameters, e.g. the difficulty or the distance.