There is only one way you might end up in Ayagoz as a tourist, and that is by driving through hundreds of kilometers of steppe. In that case, you might be hungry, thirsty, sleepy or just in the mood to see some people. In that case, you might want to stop over in Ayagoz.
Beyond eating and sleeping, there is little of interest in the town. Ayagoz is a typical picture of industrial and agricultural decline in Kazakhstan after the fall of the Union. If however, industrial ruins are of interest to you, some joyous moments lie ahead.
Ayagoz is on the road between Almaty and Ust-Kamenogorsk. Emanating west from here is the road to Karaganda, a real challenge for offroaders by the sound of it (I have never been myself).
The center of Ayagoz is Abay street, running west from the train station. Aesthetic highlight is the Kozy Korpesh & Bayan Sulu park, which pays tribute to a local legend about a tragic love.
Eating and sleeping
I suggest to buy food in the bazaar or the shops surrounding it, and continue on your way. If you do crave for a restaurant experience, the basement wedding hall below the Keremet shop offers a daring interpretation of Italian pizza, along with more traditional Central Asian classics.
I never slept in Ayagoz. If you know something of interest here, do let us know.
If you do not need food or sleep, I suggest skipping Ayagoz. All locations mentioned are marked on the OSM map.