(This picture is from Atyrau on the Kazachi Caspian Sea coast, so not technically Astana; but you probably wouldn't need to look far to find similar in Astana)
You'd probably struggle to find something exactly like that in Astana, if only because Astana was basically built from scratch to be a purpose built capital city just because Nazarbayev wanted a different capital city;
Not quite true. Akmolinsk/Tselinograd/Akmola/Astana does have some history. Officially, it was founded in 1830. There are still Soviet streets like this over there
And even pre-Soviet places like this (apparently, the building currently houses Ukrainian embassy)
and
There are still quite decrepit looking parts
Most of it I take from this pretty good overall survey of the surviving pre-Nazarbayev Astana over here (in Russian, but the pictures talk for themselves):
http://varandej.livejournal.com/456406.html