I'm not sure about Long Island, but I did go visit a breeder up in Hudson, NY. Here's a picture of the beautiful puppy I met. His temperament was wonderful. I almost got him for myself, but the timing wasn't right.
Also, you can look at this website. It's a list of breeders who are recognized by the founders of the Australian Labradoodles- so you know they are reputable. Internationally Licensed Breeders
That's not to say that others aren't reputable, but this is a starting point. You can also do a google search. I think I found a breeder on Long Island, but I don't remember who they were. If you're looking for a breeder near you, then you can ask to visit the property. Most breeders won't let you see the puppies, but they should at the very least let you see where the puppies live, etc.
The best advice I can give you is to start talking to the breeder, those that you feel confident with instantly should be your top choices.