John just came back from New York for a school competition game.

Is the sentence above correct?

Thank you
Competition game - don't use both words.

This sentence does not mean that the game was in New York. The game is wherever John is now. Is that what you wanted?
Students: Are you brave enough to let our tutors analyse your pronunciation?
Thank you very much Nona!

John came back from a game in NY.

Is the above sentence correct?