Match each state with the most populous city in that state that doesn't share its name with any other incorporated city/town in the United States.
Example: Denver is the most populous city in Colorado, but several other states have incorporated cities/towns named Denver, so continue down the list of most populous cities in Colorado until you find one that's name is not shared with cities in any other state.
For a few I had to go beyond the tenth most populous city to find one with a unique name.