Kyzylorda sits roughly 200 kilometres from the Baikonur Cosmodrome, the world's first and largest operational space launch facility. It was from Baikonur that Sputnik was launched in 1957, Yuri Gagarin made his historic first human spaceflight in 1961, and where Russian Soyuz rockets still carry crews to the International Space Station today.
Visits to the cosmodrome require advance organisation — it is a restricted facility leased by Russia from Kazakhstan and you cannot simply turn up. Specialist tour operators in Almaty and Moscow arrange access, and some operate guided tours timed around rocket launches, which is an extraordinary thing to witness. If you are serious about visiting, research tour operators months in advance and expect to pay premium prices for launch-viewing access.
Even from a distance, the vast flat steppe around Kyzylorda gives you a visceral sense of why this location was chosen: endless flat terrain, low population density, and the latitude that allows rocket payloads to take advantage of the Earth's rotation.