1. He moved to New York last year.

2. He moved into New York last year.
3. He moved in New York last year.
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Is #3 not correct?

Sentence 1 is the best one to use.

Sentence 2 is OK if you mean he lived in another town or city and then moved into New York City.

Sentence 3 is correct only if you mean he lived in New York and then moved somewhere else in New York.