They organize great trips in Kazakhstan, some of them to places where is difficult to go on your own (in KZ you need special permits to visit some areas). I suggest you to visit the eastern part of the country. Or, if you don't have that much time, just do some excursions around Almaty.
I also suggest to move around inside the country by train. It takes several hours (like 30 hours to go from Almaty to Ust-Kamenogorsk) but Kazakh people are so nice (unless you are a girl alone in the train!) that it's a great experience.
Address:
71 Zheltoksan Str. / corner of Gogol Almaty Gorod Almaty Kazakhstan
