The ones I have used are in Western Suffolk County, which might be too much of a drive for you:
Dr. Heidi Hoefer (Board Certified) Island Exotic Vet Care www.heidihoefer.com 591 East Jericho Turnpike Huntington Sta. NY 11746(631) 424-0300 Dr. Jonathan Mehlrose, DVM Veterinary Medical Center of Long Island www.vmcli.com 75 Sunrise Highway West Islip NY 11795 Just east of Rte. 231/Deer Park Ave(631) 587-0800
Dr. Hoefer is my regular vet and is board certified. I am happy with her, though she has only done routine checkups for my Green Cheeked Conure and Red Bellied Parrot.
Dr. Mehlrose handled an emergency, when my GCC was injured and I was very pleased with him.
The Long Island Parrot Society has a list of local Avian vets, including several in NYC.