I suppose you've already looked into stopping payment on your check, and it's too late (she already cashed or deposited it).
Before you actually sue, you can (and probably should, if you haven't already) send her a "demand letter" by certified mail, return receipt requested. The letter should ask her for your money back, explain why she owes it to you, and give her a deadline to return it to you voluntarily or you will sue. Keep a copy of the letter for yourself so you can include it with your other evidence if and when you do sue. One thing that might help persuade her to pay you before your deadline would be to include a copy of the small-claim filing form, filled out except for the date, to show her that you are serious.
Then if she doesn't pay I guess you'll have to sue her. According to this helpful court-system webpage, you're below the $5,000 limit for filing in NYC small claims court. It says you can sue where either party lives, but I think that's only if you live in the area covered by the NYC small claims system.
I see that your user profile shows you're from Pennsylvania; in PA, you have to sue where the defendant lives or where the controversy arose. It's better to sue where the defendant has assets and/or income anyway, since you may well have to enforce your judgment by filing for wage garnishment and/or bank account levy, and a judgment in a different state would have to be "domesticated" first (an extra step in the process).