We had family in tampa so we visited a lot. T
@Hootenany has a great list. I can personally attest to the Clearwater beache (that's why you're there, right?), the Clearwater Aquarium, a Tampa Bay Rays game (go out and feed the sting rays in the bleachers!), Honeymoon Island (bring a gallon of mosquito repellant if you plan to hike) and swimming with the manatees. The manatees are less plentiful in the summer but there are still there.
I would add the following:
* Columbia restaurant in Ybor City. It has great food and when we went they had flamenco dancers.
* Weeki Wachee Springs. It's old fashioned authentic Florida fun ... with mermaids. It reminded me a bit of the old River Country at Disney.
* Fred Howard Park Beach. It's a lazy, laid back place with plenty of parking. Your kids can also rent stand up paddle boards and kayaks there.
* Invest in a cooler while you are there even if you end up leaving it behind.
You're going too early for the Manatee Viewing Center south of Tampa, but I thought I would include it for others reading:
http://www.tampaelectric.com/company/mvc/