As mojo says, ILADS (International Lyme and Associated Diseases Society) is a good source. If you email them at contact [at] ILADS [dot] com and tell them where you are (NYC) and how far you can travel (tho you might want to just start with NYC and see what comes back), they can send you names.
These docs are members of ILADS, the main voluntary group of MDs who understand Lyme for the misunderstood ailment that it is. There is no test to join ILADS, and I have read posts in various places that some docs were not so great ... so it's not a seal of approval, but it's a very good place to start and is what I would do.
As mojo says above, just searching online can find some good sources of help. LLMD isn't a title or degree, just patient slang meaning a doc who thinks progressive thoughts about Lyme rather than the two-weeks-of-antibiotics-and-you're-well-no-matter-how-sick-you-are approach that nonLLMDs usually take.
Let us know how you do -- best wishes --
I have heard of a few good LLMD (Lyme Literate Dr) in NYC. Just google LLMD in NYC and some names come up for you. In addition you can go to the ILADS website and email them and ask them for some names.
Let us know if you have any other questions.
This doctor isn't in New York City but is one of the best----Dr. Steven Phillips. And another member recently got an appt with him.
http://www.theridgefieldpress.com/20415/lyme-disease-doctor-dancing-veterans-bank-executive/
There's a thread here that might be of use to you--- also not in NYC but I'm betting that getting in touch with some of the people mentioned in some of the articles in the Poughkeepsie Journal could give you local knowledge.