Where are you trying to add the address? If you're trying to add it on PayPal, note that you cannot add a foreign address in your PayPal Profile page.
Go to My eBay > Account > Addresses and add the NY address under your Shipping Addresses. Click on 'Make Primary' next to the NY address.
When you purchase an item, you'll see your primary shipping address on eBay at the Checkout page (under 'Ship to') before you log into PayPal to pay. The address entered on the eBay checkout page and submitted with the payment will appear on the PayPal Transaction Details page as your shipping address.
Some sellers insist on sending purchases to your "PayPal-registered address" or your "PayPal address". These sellers are unaware where the address shown on the PayPal Transaction Details page actually comes from.
By the way, check if the UPS store will accept shipments sent via USPS, FedEx, etc. I've heard of packages being refused by (some) UPS stores, because the items were sent using USPS, FedEx, etc.
