Aktau is the type of city U2 may have been talking about when they sang about a place where the streets have no names. The city is divided up into largely unlabeled and chaotically numbered districts including district 9. These are called "micro-raion" in Russian, which even Kazakhs use to describe them in Kazakh.
There is no marshutka bus map in existence, but taxis are plentiful. Flag fare should be 200 Tenge to anywhere within the city center, but this is often 300 Tenge for foreigners. Most cars in Aktau will stop and pick you up informally and there is no need to wait for an official taxi to pass by. Official taxi drivers are usually from the Caucasus, and they rarely speak Western European languages. Locals driving newer cars are a better bet if you aren't comfortable communicating in Russian or Kazakh. When you get in the car, you can simply say 'micro-raion' and then state the district's number in Russian. Afterwards, say the building "Zdanie" or apartment building "Dom" followed by the number. Addresses in Aktau are generally written as follows: 14-42-30, where 14 indicates the district, 42 indicates the apartment or commercial building and 30 indicates the apartment number.
If you should choose to experience a decrepit form of transportation, you can pay 25 Tenge for buses and 35 Tenge for marshutkas. You will see them plowing their routes on the three main roads in Aktau north and south coastal, middle north and south road, and the eastern north and south road.
