I suggest that you pursue through City Data. Post your question on that site. You will receive a spectrum of broad answers from people that live in the Tampa Bay area.
If you are not familiar with City Data, this is a site that allows you to research cities and towns throughout the United States for information just like you have asked.
As a licensed Realtor, my answer has to be broad to encompass all areas. I think that you will discover pertinent information on the City Data site that might provide you with the insight that you are seeking.
Do you know what price range you want to stay below?
Depending on your price range, you can be at the gate in 15 minutes from several nice neighborhoods. I can highly recommend the following:
The Eagles 33556
Countryway & Charleston Corners 33635
Carrollwood 33625, 33624, 33618
You're welcome to browse "like a Realtor" with a free Listingbook account on my website:
All the best,
Alma Rose Kee, PA
Future Home Realty
There are many good neighborhoods near the airport, it just depends the length of driving you want.Send me an e-mail on what exactly what you are looking for in a home. Gated, pool, gym..size of the home etc..I am a specialized buyers agent.