Have you looked into Coinbase or Gemini? As far as I know they have succesfully applied for the BitLicense. Even NY traders and miners should be free to use those.
This user is correct, Gemini can service New York residents; as I'm sure you're aware of by now it is not illegal to sell, use or trade bitcoins in New York, but it is difficult for a business to serve you.
I personally know New York residents that regularly use Coinbase and Gemini too move their coins around and there are no restrictions on selling, buying, withdrawing or depositing that is exclusive to New York.
The restrictions in place in New York are just another way for governments and big business to attempt to manipulate, control and exploit the already thriving bitcoin markets, because it threatens their current infrastructure. They would do anything in an attempt to stifle bitcoin until they can create a "feasible" alternative, or force it to fail with their targeted investments.
Simply google "US Bitcoin Exchange" or "New York Bitcoin Exchange" and start researching which one sounds like the best to you; that being said there are users around here that would highly recommend against using exchanges at all, calling them "economic suicide" because of past failings of exchanges. Be warned that exchanges are not as safe as handling the coin yourself, but that is the price you pay if you're living in New York and dealing with Bitcoins.
That being said, I believe certain websites do not refuse service to US Residents because they do not have KYC regulations so there is no way for them to know where their customer reside, however these businesses tend to refuse service to US IP addresses. I'm not sure if the liability falls on the individual, business or both (you'd have to check your legislation/jurisdiction), but this may be an option; I haven't looked into it enough to suggest it personally, but there are many who do this.