Beer
Tien Shan
Local brew brewed in a modern factory by german brewmasters - pretty good.
Russian Baltica
Numbered from 0 to 9. there's no alcohol in baltica 0, a lot of it in baltica 9. numbers 3 and 5 are quite good and close to what most people are used to.
Alma-Ata
Be sure to sample Alma-Ata beer, brewed in Almaty.
Karaganda
Two other Kazakhstani beers worth trying are Karaganda and Shymkent. There was a time that Shymkent beer Zhigulovskaya variety was one of the best in the Soviet Union. It has a unique flavour, brewed in a factory built by Czechs. Quality may have declined in recent years, however.
Tea
Is widely available, mostly very good and often quite strong. if you are on a budget this is the thing to order with your food. tea is culturally important in kazakhstan - "chai" time is one of the most important things a visitor can engage in to learn about the culture.
wine
Try the local variety, a good one can be had for less than $ 4.00 a bottle. Bebigul is perhaps the most consistently good wine, and it comes in a semidry red or semidry white. Foreign wines, even Georgian ones, are very costly. Do not drink wine in restaurants, it's usually sickly sweet and very expensive. Also, many expensive, imported "wines" sold in stores even reputable stores are actually well-made counterfeit labels pasted on bottles of red-tinted water, so beware! It i spot luck as to if a bottle of white will be served chilled, so make sure you check before they open it.
vodka
Good vodka at 4-5 $ per bottle - an alcoholic's paradise. In restaurants that do not usually cater to foreigners you get 20! cl if you order a vodka, smaller servings not available.
Buy a bottle of Kazakhstan Vodka to take back. It is in a pretty bottle with a picture of Kazakh hunting with a falcon seen through a "window".
Try Edil vodka, which is made with the pantacrene of local deer antlers.
You might want to stick to Glavspirttrest vodka imported from Russia. Smooth taste and no hangover.