Don't take it too hard that these people won't get back to you. It can be frustrating though; been there, done that. E-mail them or call them more than once. It also really depends on how fare you are willing to ship/travel. You will have more options. Living on the East Coast you should have quite a few options provided that you're willing to drive a couple hours or so. Might not be as easy if you're sticking to the city. But, absolutely a viable option. There are not usually litters around this time, and then the breeders get busy, but keep at it.
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Easy route = Facebook page "Basenji puppies" - most of the litters are out of country, but you can find the occasional US litter - or adult - and it's easy to get into contact with the breeder. Haven't seen any NY
litters though.
Medium route = keep doing what you are doing in contacting breeders (Basenji.org breeder referral). It may be that your message was too short? But, if not, then not your fault at all. Just them not responding. Some of the breeders have a preference = phone/in person contact/ or e-mail. So if you don't hit their 'personal preference' they might not bother.
Sketchy route = Pet finder (or craigslist) ; I would screen any/all dogs on there very carefully. Too many puppy mills and scam artists....but you can find legitimate sources as well. NYC should have lots of basenjis around that area.
Hard route = BRAT (Basenji Rescue and Transport) - Or other rescue. You wouldn't be getting any dog immediately. But sometimes they have rescue dogs that aren't officially on their websites. Never hurts to e-mail the NY coordinator and ask.
Hoped that helped slightly.