There are few good musicians in Atyrau, with the stand out exception and muso being Muslim, who can play - basically - anything, and in any style. Dinner jacket on a grand playing Oscar Peterson..or jeans and t-shirt laying down Hendrix on a bass guitar. But his real instrument is a fiddle.
Nowhere is reliable but try Rennaissance (Champions Bar) on a Friday evening from about 2100 onwards. Starts with some Phillipino lads playing jazzy easy listening then gets better/raunchier depending who drops in. Keep an eye out for Chris who plays trumpet and sings a la Louis Arnmstrong. Also Helga (Kazah version - blond dyed hair, large chest ) who sometimes sings before her later spot at Tomiris.
Wed and Sat go to Tengri, for music and a lot worse or better depending on yr inclination. don't take your wife. or girlfriend. And like smoke. Take yr boss. Tengri runs from 2000 ish to about 2400.
Then there's GnR which specialises in a variety of things (tautology warning) but on the music front its having an average, though reasonably competent band on every Fri and Sat playing the same set; for about 6 - 12 nonths at a time. So once they're into the second qtr, they're competent.
Not to be missed (somewhat tic here) is the Riverside Bar, beside Europa Residences - on a Sunday evening. Sometimes (just sometimes) everything clicks and its really good. Mostly though..hmm. But the beer is cheap and the bar food is good. Pizza's and Honey Chilli Chicken.
There is virtually NO original or Kazakh music to be had in any of the standard Atyrau "city" centre places. For that either go to a pukka concert at the "Dram Theatre", over the bridge end of Abay Str..or the other theater in Zhyl Gorodok (by the footbridge). In summer time there are plenty of open air shaslik joints with s singer / musician who can be quite enjoyable. There's also a bunch of restuarants - Russian cabaret style places (where have you ben before Atyra ?) which sometimes are good, depending on your mood and recent consumption of life expectancy reducing drink and women.
If none of the above appeals - go for a weekend in Aktau/Istanbul/Baku/Almaty
Trust this hekps