Welcome @Josephine Giordano ,
As a fellow New Yorker, I can say I was surprised to see the transformation Brooklyn has been going through on a recent visit. From Williamsburg, Bushwick, Greenpoint and to my surprise Fort Greene. Towers are going up at a rapid rate and the cost of living there has gone up exponentially. So I can see how easily it is to be priced out of the market there.
I believe you are thinking in the right direction on investing out of state. I know many New Yorkers who can't afford to live in NY move to areas like Atlanta, Orlando, and South Florida. Those cities have become somewhat of a sixth borough for many New Yorkers especially in the South Florida area. Plus Northerners are getting fed up with the cold Winters and shoveling snow. We have tons of people move here every year from up North. Weather and affordability are usually the driving factors.
As you pinpoint places to invest in Florida I would also consider areas like West Palm Beach, Fort Lauderdale, Cape Coral, Sarasota, and even Tampa. You can find some really great properties in those places and set your rental rates for a good return. In some areas, you can even buy new construction which can end up being a better deal than buying a resale.
Miami does have higher rents compared to the other cities I have mentioned due to population density. Infrastructure and job growth. Proximity to the beach and the lifestyle. However, the cost to acquire a property that will allow you to achieve those returns is a real challenge. Not impossible but will take some effort.
As far as property management is concerned. There are many of them here that specialize and look after investment property for people living in other states or abroad. You will need to Google them for reviews and interview them to see if they will be a good fit for you. Most take 10% of rents but it is all negotiable.
Good luck on your journey!