The InterContinental (former Regent Ankara) and Rixos Almaty are both great hotels. There is no Hyatt anymore, it is now rebranded to Rahat Palace, and I have not visited that place since the new ownership.
If you gonna be there just for a short stay, or the budget has some limit, the Holiday Inn across the street from InterContinental is fine. Just book the larger rooms. About half of the price and ok breakfast.
I agree, the Berkut seems to be pain now-a-days, have to try the World one next time.
Have fun!