Hello dear!
I'm not a NY local, but I took the liberty of doing some research on your behalf...
I found two Amy's Hallmark (corporate store) in Manhattan located at
7 Hanover Square, New York, NY 10004 (phone number 212-825-1625)
AND
Rockefeller Center, 30 Rockefeller Plaza, New York, NY 10112 (phone number 212-956-9113)
They are open 8am-7pm Monday through Friday, closed Sat and Sun. I called the store and they are carrying Rainbow Brite stuff- they currently have the large RB doll, Twink, "some horses", and lots of itty bitties. I asked if they were to run out if they will be restocking, and she said yes- but more importantly she is willing to put items on hold (though I don't know for how long, perhaps days at least).
Two other franchise owned stores located at:
625 8th Ave #201, New York, NY 10018 (212) 564-6030
820 2nd Ave, New York, NY 10017 (212) 599-7200
Hope this helps! If you know where you're staying in Manhattan, let me know and I can call the nearest store for you to check on their inventory.
pq