South Tampa is a good place to look, very good public schools and close proximity to all major sporting events.
However, traffic is horrible and the neighborhood is prone to flooding. You also will have very little to no back yard.
My dad recently purchased a 1,100 square foot home for $299,000.
If you want a little more home and land, for the same price, look in the Odessa/Lutz part of Tampa. Many of the wrestlers/pro athletes live back there. Also, you can take the veterans into St Pete, but then again, traffic on that rode is brutal during rush hour.
As far as St. Pete, no clue, hardly ever cross over that bridge. Have heard good things about Palm Harbor area