I've been to Kazakhstan many times and stayed at several places in Almaty. The Hotel Kazakhstan is my top choice for several reasons: It is in a prime location in the heart of the city where you can easily walk to many of the main attractions--the Green Bazaar, Panfilov Park, Ascension Cathedral, Kok-Tobe funicular, the opera house, etc. Almaty is a city made for walking!
The hotel Kazakhstan is at a higher elevation, especially if you're in an upper floor, so the air is much fresher. The big windows in the rooms also open wide, so you can let in all the fresh mountain air.
The complimentary breakfast is vast, with all the usual breakfast items plus many hot dishes, fruits, salads, etc. There are several good restaurants in the Hotel KZ complex, and there are dozens of excellent restaurants nearby.
Directly behind the Hotel Kazakhstan is a peaceful and shady city park where you can relax. It also has a great children's playground--excellent if you are traveling with kids.
If you are new to Almaty, you will want to ride up to Kok-Tobe on the funicular, and the entrance is directly next door.
I found the hotel staff extremely helpful and friendly. (Not all the staff are equally good with English, so you should have patience too.)
Lastly, the room rates are a great bargain (I had a "Superior" room on the 24th floor on my last visit, which had terrific mountain views.)
There are many much more expensive hotels in Almaty, but the Hotel Kazakhstan is my personal favorite.