I've been in the Ft. Lauderdale area for 16 years and started looking for a place to finish raising my kids. I agree on Sarasota - in addition to the traffic near the beach, it's not cheap (unless you're 5+ miles inland) and I didn't find it kid-friendly.
I settled on Northwest Florida (AKA - Gulf Coast/Panhandle/Redneck Riviera), specifically the area between Panama City Beach and Destin.
Great salt water fishing, plenty to catch in the huge bays just inland and many fresh water lakes within 100 miles. Housing prices and styles range from stupidly expensive on the beach to very affordable as you move inland just a few miles.
Shopping and services including health care are adequate, but don't have the range of choices I've been accustomed to.
Once you're 5-10 miles north of the beach, you're in the rural South, and that won't be to everyone's liking. Fine for me, though.
The major downside I found is the summers are crazy with tourists. Traffic moves slowly on the weekends and beach parking can be difficult. Both are manageable if you plan ahead though.
Plus - no state income tax