The Gulf Coast is busy, especially as far south as Clearwater. Further north, the coast is more a collection of fishing villages and small towns. Maybe not urban enough for kids. Very conservative, rural areas but lots of natural beauty.
My area - North Central Florida and specifically, Gainesville - has the best of both worlds. It's less than 2 hours to either coast, but we are also surrounded by lakes and rivers. Gainesville has a major University and another large state college. We have lots of cultural events and, of course, sports, as well as museums and art venues. The vibe is definitely younger than many places in Florida. We are known as The Tree City because our county goes to great lengths to preserve trees so we don't become like South Florida.
I live in a densely populated neighborhood with a nearby elementary school and yet, we are on a lake, surrounded by nature and protected woodlands and wetlands. There are other places in Gainesville that have a charming mix of nature and humanity.
Being inland also protects against hurricanes and tropical storms - definitely something to consider. They lose a great deal of their punch as they travel across land to reach us. Earlier in the summer, Hurricane Elsa came ashore on the west coast as a hurricane but was a tropical storm by the time she reached us. Same with Hurricane Irma in 2017.
Ocala, south of us, is also a nice area, but definitely, leans more towards the older generation. It's also a major horse-breeding community.
I'm more than happy to answer any questions, if I can. I also lived in Melbourne on the east coast back in the 70s. I loved it there but haven't been back in years. I've been in Gainesville or in the rural area outside of Gainesville since 1983, so I know it well.