The controllers in Almaty actually speak English very well, though accented. All you have to do is ask for the QNH and you can fly a regular approach. It has been my experience that they ALWAYS keep you high for the approach (when approaching from the China side of things) and getting down and being on speed is a struggle, at least in a 747. Not sure what kind of plane you are flying or how well it can plummet on demand, but it might be advantageous to ask for lower any time you can. They will give it to you almost all the time as long as you have the terrain clearance.
Speaking of terrain, of course, just be mindful of the Tien Shan mountains to the south and east of town. Flying towards 20,000 foot peaks close to town is not my idea of fun.
On the positive side, mountain-wise, you might want to rent a car and driver for the day while you are there (not too expensive) and drive up to the Chimbulak ski area in the hills. HUGE Olympic-sized outdoor ice rink (Medeu), scenery, hiking, etc. Alternatively, you can stay in town and take the little cable car up to the area by the big T.V. tower (Koktobe). A nice view and there is some stuff you can walk around and see there. Also, if you are looking for souvenirs, etc., find the Barakholka market. You can get things cheap there. There's also a huge green market where you can get everything edible...if you are a fan of horse sausage, that's your place.
Overall, I like Almaty a lot. The people there seem very friendly, many of them speak English, the food is good (just gotta be adventurous and know where to look for it), the city itself is quite green and park-like. Though it does seem a bit deserted since the capital moved to Astana. You kind of walk around thinking that everyone is out of town on vacation or something. Have fun.
