The sign for "New York" is to slide a "Y" hand forward
and back on the palm of the non-dominant hand.
If you need to specify "New York, city" vs "New York, state" you can
add the CITY
sign or the
STATE sign.
NEW YORK:




Here's another view:
.


You might see a version in which the right "Y" hand slides
forward and back one time:



Animation: NEW-YORK

NEW YORK CITY:
(Model: Byron Cantrell)
You can learn
American Sign Language (ASL) online at American Sign Language University ™
ASL resources by Lifeprint.com © Dr. William Vicars