I stayed in Urgench for two hours and it was too long!
By contrast, there are many buses leaving to Bustan in particular. There, I discovered half a dozen cities/castles/forts in ruins! (In the guides, they say there are 20 of them, but I only found 6.) I am a person who is really interested in history, so I really enjoyed these visits. Try to take advantage of a guided tour, because their explanations about the sites will only be the best.
The best known of the ruins, Ayaz Qala, is made up of three fortresses located up high in a mostly desert area, where you can see the lake's shores. Getting closer to it, the pools of saltwater succeed one another and make the atmosphere particularly arid. On returning to the fortress, you can always spend the night in a yurt camp, set up only for tourists. The welcome is still rather nice!