My husband and I made the reverse move--he was born and raised in Tampa/St. Pete and I was born and raised about 45 minutes south in Sarasota. Now we live in NYC.
Neither of us had trouble finding work in FL. Salaries were significantly lower for both of our occupations in Florida than they are in NYC, but then, COL is much lower in FL, so it really balances out, or it has for us. We find ourselves with the same percentage of savings rate in both locations. So I wouldn't necessarily make the move JUST for an increase in savings.
Personally, I prefer NYC to the west coast of Florida. When I was living on the Gulf Coast, I felt as though the vast majority of the population were either college students or older retirees (65+). I agree with Samala--whether you will like Tampa/St. Pete really depends on what type of lifestyle you are looking for. Previous posters are correct that there are a lot of outdoor activities available in the area. There are fewer cultural events and more chain stores/restaurants than what you are accustomed to in NYC.
If you are just looking to move to Florida in general, you might also consider the Jacksonville area. It is a much larger city with more diversity in its offerings and a younger population (my husband and I lived there for a few years as well). It's only about 3-4 hours' drive from Tampa, so if you have family there, it's not so terribly far away.