Urgench- Nukus is 80-100k. I paid 100k since I was late and was only two cars left. They go from "Dinamo" stadium (I think is now called Xorazm Stadium). So something similar is back.
As for Moynaq in Nuksu they were asking for some crazy numbers like 200k so i all send them to hell and went with bus.
From bazaar in Nukus you can go everywhere with marshrutka (damas);)
. Go to bazaar and ask for avtovokzal. When you will step out of Damas, bus for Moynaq is just behind wall/shops aprox 100m away. Bus is 20k last one goes at 11am. From Moynaq at 3pm.