Personally I think St. Petersburg has it all over Tampa as your final destination.
St. Pete has the
beaches,the
Salvador Dali Museum, it also
the Pier downtown, it has the old classy hotels like the
Don Cesar and the
Vinoy which are worth visiting for lunch or something... you can drive north for about a half-hour or so to Clearwater or go a little farther to the sponge docks at Tarpon Springs for a day trip. You'll find a lot of kid-friendly things at all of these.
Tampa's got
Ybor City, which is pretty cool for strolling around, shopping, eating, etc. Not really sozlet-oriented, but does have some interesting history as the Latin quarter. There's old cigar factories they've turned into malls -- that sort of thing. If you're there, be sure and go to the
Columbia Restaurant and order the
paella.
And if you have time to drive a couple of hours,
Weeki Watchee Springs has the mermaids and the manatees and lots of kiddo entertainment.