You first have to determine whether you are working in Florida for your own convenience or for the "convenience of the employer." I don't understand what you mean by "don't think I meet the convenience of employer tests." Are you working in Florida because you prefer to live there, or are you there because your employer needs someone in Florida, or requires you to work remotely? The answer to this question will determine how much of your income is subject to New York tax.
But your W-2 is a mess. It's impossible to have New York City wages without any New York state wages. Any income that you earn in New York City is also New York state income. But worse than that, nonresidents do not pay New York City tax at all, period. The convenience of the employer rule doesn't matter as far as the city tax is concerned, because nonresidents are not subject to New York City tax under any circumstances. No city tax should have been withheld. I'm not sure what you do about this. I think the ideal solution would be for the employer to give you a corrected W-2 or a W-2c removing the entries in boxes 18 through 20, and give you a refund of the city tax that they improperly withheld.
