Kok-Tobe is the name of the hill behind the Hotel Kazakhstan and the Republican Palace in Almaty. If you can't see the hill you should at least be able to see the TV Tower from most parts of the city. This very TV tower sits on this very Green Top or the Green Hill (it's the kazakh translation for Koktobe).
If you are too late in the day to go anywhere outside Almaty, this is the place to come. You'll see the most amazing sunsets as the view point is facing the right way.
It takes only ten minutes to get there by cable car that starts off next to the Republican Palace before the Arman cinema theatre. It is a bit costly to reach the hill, but you'll be away from the city. And that's what you want, aint it?
This Kok Tobe Map is easy to use. You can use + or - to zoom in or out and the arrow are handy to move to all 4 sides letting you see more of the city.
You can also get there by bus. Check the route of the Koktobe bus here.
There are some great view points there over Almaty and over the other side of the hill to more green hills, provided there's not much traffic through the day.
If you are the Beatles' fan then you can have a chat with all four of them at their bronze monument.
If your travel budget is limited I suggest you take your snacks and drinks with yourself, as it can be quite expensive buying them on the spot.
Apart from looking over the city when you are on Koktobe, you can also enjoy:
By the way you can also go up there on foot. I did it a while ago, you know what, I wouldn't do it again. But you might?