I don’t know if he can ban flights from just one area, and as others have mentioned, people will just go to another airport. They need to check the ID of every passenger of every flight to make this mandatory quarantine have the smallest chance of working. That may or may not happen - I am not privy to the intricate details of how this will be accomplished.
I would like to see the airports closed completely. If they can do it for hurricanes they should be able to do it for a pandemic. I know it’s not possible to close the roads because of trucks needing to get through with food and other necessities, but if there was a way, I would be for it. In an ideal scenario, every person in the country should be sheltering in place, with supplies so grocery stores can be closed as well. The only people who should be working are medical and first responders, for three weeks. That hopefully brings the community spread to a halt (especially if the few people who must work shelter in place at work). Not just NY, not just FL, but everyone, everywhere. Without the ability to test everyone, a firm nationwide quarantine is our only shot, and it gets more difficult each day we go without one. I do not have high hopes at this point.
I don’t blame anyone for wanting to escape a sea of contagion, wherever they live. I just don’t want a sea of contagion in my neighborhood because of it.