There are numerous places to wet a line in this area. It helps to have a boat, but is not necessary.
Saltwater- If you would like to try your luck on catching one of our delicious Tampa bay fish, your best bet is going to be the Courtney Campbell Causeway. A couple of other good spots are Upper Tampa Bay Park and Cypress Point Park. You should be able to fish from the dock in either of these places and if you are dedicated, wade out into the bay. It is unlikely that you will be killed by anything, but if you try this without shoes it will be a while before you walk without assistance. The oysters will shred your feet. If you know nothing about fishing, go to any bait shop and they will help you get set up.
Freshwater- There are numerous small freshwater lakes peppering the West part of the County. Most of these lakes are going to be private and access will be restricted. One good place to try is Lake Rogers Park. Here you have two lakes and a boat ramp.