If his current residence is NY I think he can file there.
As part of the divorce process both of you will probably be required to file financial disclosures including assets, income and expenses. If you think he's going to claim no income you should be looking at collecting any evidence you can to assert that his disclosure is incorrect. Bank deposit records or anything like that will probably help.
Even if he really does have no job and no income, most courts would "impute" at least a minimum wage to him. If he's got some kind of employable skills they'll look at the market for those skills and might impute a higher income (for example, if he has experience installing drywall AND the prevailing wage for drywallers in his area is $XX AND there appear to be drywalling jobs available in his area that he could compete for, then the court will say that any spousal support claim SHOULD be based on his ability to earn $XX, and his choice not to earn at least that is his problem.
It sounds like the best thing for both of you is to just make a clean split and get this done as quickly and cheaply as possible. Hope you can make it work out.