Don't ignore the lawsuit -- you will be defaulted.
You can be sued in the state in which you were living and in which you incurred the debt, even if you have since moved. You can try objecting to the court's jurisdiction, but you should not expect to succeed. A lawsuit cannot be transferred from one state's court system to that of another state.
Given that they would have to domesticate the judgment in New York to enforce it in that state, their lawyers may be more willing than you expect to dismiss and refile in New York, or to negotiate a settlement and payment plan. You won't know until you ask. If your financial situation is dire, you also have the option of bankruptcy.

