Florida does not have a state income tax, therefore nothing to file.
New York does have state income tax. NYC may (likely does) have a city tax. Income earned in a state (and some municipalities) generally requires the filing of a tax return with that taxing authority.
You may be able to deduct on your federal tax return traveling expenses incurred while away from home. A professional can help you determine whether you qualify, and any other applicable deductions to ensure you pay only what is legally required.
I highly recommend using a professional familiar with NY, NYC and federal income tax laws. It is usually well worth the fee. Ask family, friends and neighbors for recommendations of a tax professional.
Too often individuals don't take advantage of every deduction they are legally entitled to and end up paying more taxes than necessary. Few can afford to pay more than is required.
Hope this helps!