I am the claimant in a small claims matter in New York City, and the defendant recently entered a counterclaim against me. However I am currently out of the state and unable to attend the court date. What happens if I do not appear?
You started it. If you don't appear and finish it, you will very likely lose your own case by default. And if the judge finds merit in the counterclaim, since you failed to appear to present a defense, then it's possible you could end up with a judgment against you for your troubles.
I would suggest contacting the court about requesting a continuance or rescheduling your appearance. Otherwise, it might just be more prudent to dismiss your case altogether (without prejudice, of course, in case you should decide to pursue it again when you can manage to find the time to make it to court).