Does an extended stay hotel qualify as "living quarters" for New York tax form IT-203?

Reading the instructions, it notes:

These living quarters would include a house, apartment, co‑op or any other living quarters that are suitable for year-round use, maintained or paid for by you or your spouse, or any living quarters maintained for your use by another person, family member, or employer.

Perhaps someone more versed in New York rules than I will know for sure, but I would suggest that an extended stay hotel is possibly suitable for year-round use. In this case I think it won't make a difference in your taxes - you said you only stayed there three months, so you won't be a full year resident since you were there under 183 days - so you may want to be cautious and complete Schedule B.