The most concise way that I can think of is: "I haven't been to any cities in the US other than New York!" I hope this helps and I hope you can see more of this beautiful country! Also, if you have more questions or want to practice more, feel free to schedule a lesson with me (my prices are very low since I'm new to italki!)!

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"Than" or "besides" are both correct, but "besides" sounds more natural to me. The singular "city" or plural "cities" are both correct, but the plural "cities" sounds more natural. "Than" would sound better if it were closer to the word "other" since "other than" is the common phrase. I haven't been to any other U.S. cities besides New York. I haven't been to any U.S. cities other than New York. New York is the only U.S. city that I have visited.