The Hyatt is fine, not to worry - food is good, if not a little too expensive & there is a good gym & pool.
Tinkhoff is within walking distance - a micro brewery (opposite the Kazakh National University) with it's metre long sausage; & there are other good restaurants around (Indian, Chinese & Uzbek) - suggest you try to get hold of a book called "Hedonists guide to Almaty & Astana" ISBN 978-1-905428-21-2. I met Lucy Kelaart (author) several times in Almaty and she has produced a good reference guide - can't say much about the Astana building site.
After discussing with the Missus, she seems to think you mean the FO you were speaking to was referring to Aktau and not Atyrau. Aktau was a closed city during Soviet times and had a Uranium mine about 50 km to the NE (which you can clearly see on approach into Aktau airport). However there is no radiation threat in Aktau city for you either.
Have fun, I won't be heading back until February - best time of year - nice and cold
only -27C in Aktobe yesterday.
Poka