I tried a few of the places I got .22 ammo from in the past (when I lived in NJ) and none would ship to NY unless it went to an FFL. I ended up having it shipped to a friend in NJ, and she brought it up for me on her next trip north.
If you have a good rapport with a local shop, see how much they want to receive the shipment for you. Some places will be quite cooperative for good customers.