Cities are really hard to reinvent. Since this one is located in an extra dimensional space/different plane though, why not take some big liberties and make it a unique one. For instance, why not get rid of Inns altogether. They're pretty overdone anyways, and you could easily have some kind of wine/smoke parlors to serve as places of gossip and gathering spots instead. Could use val's idea of floating globules of liquid instead of having glasses/mugs. Why no Inns though? How bout, the city is sorta like a giant gyro, built on a flat surface, mirrored on the other side with stairs leading down onto the other side.
Now I know you said the laws of physics applied for those who lived there, but that doesn't have to be true with the city itself. So instead of sleeping, you walk down the stairs into the night portion of the city. The sky could even be painted on the inside of the globe for an extra sense of surrealism, with big clockwork arms that move the sun and the moon. Then when you walk up the other side again, you feel as refreshed as if you had slept. Meanwhile, the city rotates on its axis, but the local gravity on both sides remains the same. Leading to some M.C. Escheresque stair creations.
To make those sun priests a bit more interesting. How bout making them some kind of clay golems, sort of like a mixture between the Japanese Haniwa and the Strandbeests made by Theo Jansen. They're not actually alive, but when the sun warms up the water in them, they start moving around in a way that seems sentient, some would even claim that they are very much alive and has an agenda of their own. But basicly they are walking shrines, offering blessings to people they pass.
That's what I've got so far, I would also recommend if you haven't seen it before, to have a look at this series;https://www.youtube.com/playlist?list=PL_9VobYoMHhBjLjSxq5vzNW_9b00VUxiE
It's kinda hard to understand what they're saying sometimes, but there's some interesting, original and surreal concepts in there, I feel.
Hope that helps.