Change the city’s race.

I have a map where each player has a designated city. How can I use the map editor to make it so that when the map is launched, players can freely choose their hero's race and city?

If I understand correctly, you didn't use "Random Town," but instead assigned a specific city. Just to clarify, is this your map, or do you want to modify an existing one?
In that case, assign a Random Town to the desired player and, in the map settings, set that city as the primary one. The player's race can also be configured there; if you set it, the player will be of that specific race. If not, and a Random Town is present, they can choose. Enable "hero generation in the city," and you're all set.
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*If I didn't explain it clearly, I can attach screenshots. 😄