From 1903 through 1952 the American and National Leagues each had eight teams. That's 16 teams that played in only 10 cities, half of which had multiple teams. 11 of 16 teams played in multiple team cities.
Boston: Red Sox, Braves
Chicago: White Sox, Cubs
New York: Yankees, Giants; Brooklyn Dodgers
Philadelphia: As, Phillies
St. Louis: Cardinals, Browns
In 2018 only New York and Chicago have multiple teams.
A hundred years ago or so sometimes when no teams in a city were in the World Series, they would play an intracity City Series. For instance, if neither Chicago team was throwing the World Series they might play against each other.
That's still a good idea. But here is another. All star teams from a city or state play. Something would have to be done about California because it has five teams, maybe two teams. But here are eight combinations, enough for a tournament.
California central: Giants/As
California south: Dodgers/Angels
Chicago White Sox/Cubs
New York Yankees/Mets
Combining any two teams should probably result in a competitive team.