I commented on another recent tip request on fishing Ft. DeSoto and Tampa Bay, and I'd offer the same recommendation here. I lived in Clearwater for several years and fished the area heavily with my father. I still have lots of family in the St. Pete area and go fishing there every year.
My best walk and wade suggestion is Honeymoon Island, north up the coast from St. Pete Beach. It's a state park, so your backcast won't be a bother to anyone like it would at St. Pete. There are essentially three options to attacking Honeymoon Island (formerly Hog Island):
The first (and best) option is to rent a canoe or kayak somewhere (not sure where) and fish the grass flats and mangroves on the east side of the island, putting in just after making your way through the ranger pay station.
The second option is to park at the trailhead for the osprey trail. Its a good hike to the north end of the island, but once you get there, there are good sand bars dotted with grassy spots which hold good amounts of speckled trout.
The third is to park at the beach on the west side of the island and fish Hurricane Pass to the south, which can be very successful on moving tides, especially outgoing tides. Or you can walk north down the beach and target cruising snook - which is best accomplished in early, early morning light.
Aside from that, there are countless sea walls, docks, piers and public parks (look for those with boat ramps) in St. Pete which can also be successful.