My wife is from Astana, KZ. I have travelled there quite a few times from NY. First thing i will say is you have to know Russian if you really want to be able to get around (I am actually from former USSR myself, but lived in USA for last 22 years). Without knowing Russian, be prepared for authorites and other opportunists to take advantage of you (mostly for financial gain). If you do travel, I highly recommend you go with someone who is a native Russian speaker, preferably someone from KZ itself since there are a lot of central asia-specific peculiarities that they will know how to deal with .
Other than that, the standard of living in Astana and Almaty (places i have been to) is on par with Western Cities. Regular people are very nice and friendly, but again, you have to know Russian to communicate. Everything else that applies to any Ex-USSR republic applies to Kz. Almaty and Astana are very safe, as long as you dont stick your nose into the wrong people's business .

As for flying - both LH and KLM fly to Almaty. There is Air Astana, which is excellent compared to both KLM and LH, the only problem is if you fly from USA like I do, you can not easily book it via connection, so if your USA-EUROPE flight is late and you miss your Air Astana flight, you are on your own.
LH flies to Astana (its actually the same flight as Almaty flight, just stop over) but the actual price is almost $500 more because LH is the only western airline to fly there, so they abuse their monopoly position. You can always get off at Astana even if you ticket is to ALA, but you will have to board at ALA because if you dont, they will cancel your entire ticket.

Feel free to post here if you want any more KZ info, i will gladly share what i know from my experiences.