I live in Lutz ,and I teach in Hillsborough County which Tampa is part of along most of the surrounding areas. The School District of Hillsborough County (SDHC) is the 7th largest school district in the country. Thus, there are many amazing schools and great areas to raise your kids. As already mentioned, Lutz is great, as is Fishhawk Ranch, and Westchase. The South Tampa area is excellent, too.
Link to SDHC webpage:
http://www.sdhc.k12.fl.us/
If you have a prospective address you can find out the neighborhood school here:
https://choice.sdhc.k12.fl.us/locator/Default.asp
We also have public magnet schools. They are often in the city, but also often very good. My DD attends a magnet elementary close to downtown, and we are VERY HAPPY.
SDHC Magnet School info page:
http://www.sdhc.k12.fl.us/magnet/about.asp
FYI - in FL the state gives each public school a grade from A-F. Here is a link to the page you can look up the school grades:
http://schoolgrades.fldoe.org/
Keep in mind the school grade does not give a FULL picture of a school, nor is it a comprehensive assessment of whether or not a school is "good." However, it gives you a decent gauge to work from when you are researching.
In the central FL area the school districts are all county-wide.
PP mentioned Land O' Lakes (LOL) - that is Pasco County and a different school district. I think most schools in Pasco are very good especially in LOL and Wesley Chapel area. St. Pete and Clearwater are just over the bridge and are part of Pinellas County - know a tiny bit about St. Pete schools and nothing about Clearwater.
I have lived and worked here for 16 years. I love it here and I do not envision ever leaving.

If you have any questions feel free to PM me.