Definitely bring along a coat/long jacket if you’re not accustomed to the NY cold. But if you can, try a warm, lined trench coat and not something bulky in case you need to shlep it instead of wear it…
While currently it’s warmish by NY standards, especially if you plan on doing a lot of walking which will warm you up, it’s still a major change from Florida weather and can be quite windy. And the weather will vary throughout the day and from day to day, so think layers.
Dark, streamlined sneakers are a good option for your feet so you walk in comfort without being too ״bold” and have some warmth in your feet with minimal sweating (unlike boots). But if there’s rain – or more so snow – in the forecast, you will likely need some type of boots.