Even though you are considered a nonresident alien under the Substantial
Presence Test for federal income tax purposes, if you resided in NYC for more than 183 days during 2017, the NY department of revenue will consider you to be a resident of NY/NYC for the entire 2017 calendar tax year.
As a resident of NY/NYC, you are required to file a resident NY/NYC income tax return which would include all income from all source include income earned during a temporary internship in WA and any signing bonus related. This is true even if your income was earned in another state.
Usually you would pay nonresident state income taxes related to your out of state sourced income and get a tax credit on your NY resident state income tax return but since WA has no state income taxes, then you would only need to income this income on your NY resident state income tax return.
For more information on the NY state filing requirements, please click on this link - https://www.tax.ny.gov/pit/file/do_i_need_to_file.htm
