I don't see why not. Most state trial courts have general jurisdiction; most any kind of case can be heard there (there are some few exceptions, such as copyright suits). It sounds not that much different from a normal divorce case. If your question pertains to diversity jurisdiction, then the proper question is not whether the state court can hear it, but whether the federal courts can: unlike the state courts, they have only limited jurisdiction.
Just from looking at the facts you've given: the damages look pretty solidly over $75,000. It also looks as though diversity is present under 1332(a)(2) (you have a citizen of a state and an alien, who can sue in federal court under alien jurisdiction). However, the Def. might be able to argue lack of diversity, if he has obtained permanent residence in the US and is domiciled in the same state as the plaintiff (maybe NY). The issue of domicile depends, of course, on whether either party possesses the subjective intention to remain in NY indefinitely.