Where's the USCG station located at? That will be a factor for the commute in the St Pete area. A significant portion of this area is truncated by US19 which can be a real bear as it's continually under construction.
I'm on the beach in St Pete beach and would never suggest it if you have young kids.
Edit: I just looked and see 3 stations. One up in Clearwater, one in Bradenton and another over in St Petersburg. If it's Clearwater then Palm harbor is nice. So is the Safety Harbor area.
For the St Pete station or Bradenton your options really open up. You can commute 275 over the Skyway for St Pete which opens up all of the locations in Manatee and Hillsborough counties. Sundance, zoned 5 acres, is nice but getting pricey.
Myakka also has lots of opportunities, both older homes as well as developments. Nice out there and would work for Bradenton or St Pete.
As mentioned the schools in the area are brutal. Pay no attention to the FL rating of schools....all lies for Fed funding. Fishhawk in Valrico has the best schools in the area but that would be a bit of a commute for you and those homes are pricey.
I'd take this area over Miami but that's me. To find the equivalent home in a decent area of Miami you can expect to pay about 30% higher and it would be good if you're a Spanish speaker. Not a hit on my Latino brothers,,,,it's just that speaking espanol in Miami really opens up the city.