Obviously in a city by the water there are going to be places to kayak, if you have one. If you are going to stop and get out of your kayak, you may wish to invest in a long cable lock to make sure that it is there when you get back.
Davis Islands. You can launch at the Seaplane basin and there are several trips that you can make from this one location: kayak around DI and check out the waterfront homes, paddle around Harbour Island and see the Port of Tampa and maybe stop for a drink at the convention center Sail Pavilion, One more trip from this entry would be to paddle up the channel and view the Hillsborough River. Fantasy Island is a small park located on the East side of the Northern Spoil Island in the bay that would be a fun kayak trip for those who haven't seen it yet. Just be careful to maintain a distance of 100 yards from the ships or docks at the port.
Palonis Park at the base of the Gandy Bridge offers a decent place to launch a kayak. If you paddle North from this point there are multiple sandbars to stop at and you could make your way all the way up to the Howard Frankland. There are plenty of beautiful homes to view along this route.
DeSoto park is a spot that you can get a kayak into the water. This is a good spot to explore McKay Bay and the Palm River. If you take this trip on a Sunday you could stop at the Thai Temple.