Move. Alternatively, consider relocating.
Actually, after looking a bit, it appears that bittrex.com has applied for a BitLicense. Volume is quite low (~5 BTC) on the XMR market, but I'm sure some tasty bids would attract more sell-side liquidity (or buy-side dumping).
Bittrex is another one.
Sad that NY consistently chooses banning over freedom, even to the point of a 20oz soda.
That's just New York City, rather than the whole state, but agree nonetheless.
Can you use a proxy to access the poloniex?
Sure you could, and in fact you don't have to provide address info for the lowest tier of Poloniex verification (limited to $2000/day withdraw). However if you keep money there you'd be constantly at risk of them potentially asking for more ID in the future. I've not heard of it happening but the risk is there. If I was a NY resident, its not a chance I'd like to take.