Is it possible to have “two” sets of tags?

No, you can’t have 2 groups of a singular taxonomy, so there is no way to separate post tags from each other without introducing hierarchy.

However, you could register a city taxonomy and declare that it’s non-hierarchical. That’s the primary difference between categories and tags. Categories have hierarchy, tags do not. Any taxonomy you register this way will have the same UI as tags.

For example, I registered a talk tag taxonomy for a CPT on my own site:

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I just set hierarchical to false when I registered it.

In general, don’t repurpose tags and categories for things, just register a new taxonomy, it saves a lot of trouble and makes your life easier.

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