I'd have to say that Futaba's palace was mine. For starters, it proved that society's villains aren't the only ones to have palaces; normal people with extreme distortion in their cognition can also obtain palaces. In Futaba's case, she blamed herself for her mother's death, distorting the true facts of what really happened and how her mother truly died. To me, this provides interesting characterization, as well as a stepping stone to discover the truth behind the mental shutdowns. Aside from this, I loved the desert setting as well as the plethora of 0s and 1s on the walls. It was a subtle detail, but it really tuned in to Futaba's talent as a hacker. And I really liked the pharaoh-like appearance of Futaba's shadow, as well as her quirkiness; in a sense, her mannerisms reminded me of Futaba's own personality, which is shown later after she joins the team.
Overall, I guess the entire palace was just really appealing to me, and it was an interesting experience.
I also like the fact it was the only Palace to go 'outside' of the Palace, like in that deserted town. I wish that part lasted longer.
Oh, yeah; that part was actually really interesting. That little desert city town setting looked quiet and peaceful in contrast to the distortion of the palace.