One, Eville, is a little town which is entirely populated by supervillains, either retired, on vacation, taking extended leave, raising children (hard to be a supervillain with the kids, after all), or up and coming in training. This place would have a school which essentially teaches supervillains a modified version of the evil overlord list, essentially how to be an evil villain while not being a stupid villain.
Two, Heropolist, is a city populated almost exclusively by superheroes, also largely retired, on vacation, taking extended leave, raising children, or up and coming in training. Unlike Eville, it does have a rather significant civilian population, in part attracted to how the schools there are the counterpart to Eville's school, in that they train competent heroes.
They not only train heroes in how to counter stupid villains, they go a step above and beyond to go teach how to counter smart villains. These schools also provide bystander classes (thus the appeal to civilians), in that they cover the dos and don'ts of getting involved with a supervillain.
I haven't really fleshed out this setting that much and what would be the details of it exactly.
But I think it's a really neat, fun idea in which there would be potential for a lot of hilarity in watching the two rival cities meet with one another. (Well one's a town, the other's a city, butstill.) And, yes. They do meet with one another rather frequently. Up to and including in high school sports. Eville's team is rather predictably The Villains from Eville Education Center (often called the Eville Villains); Heropolis has multiple schools but the most bitter rivalry is with Hero High's Crusaders.
It's just a world which I think would be a lot of fun to explore, but I haven't quite given it that thought yet.