Persona dungeons tend to manifestations of the subconscious or general culture. In Persona 3, they only show up in the "Dark Hour" at midnight. In Persona 4, you have to enter the TV. Here, I'm thinking they appear at midnight.

As for dungeons, well, it depends on general American pop culture. We see steam baths among other things in the Persona series, so it's probably malls, sports stadiums, TV sets... who knows, we might even get an evil(ler) Walter White as a boss :lol