I take trips down to Tampa once or twice a month as my parents; in laws; sister, her husband and nephew; SIL, her husband and two nephews plus a bunch of cousins, aunts and uncles all live in the general area scattered around Brooksville, Lutz, St Pete, Ruskin, Lakeland, and Tampa itself. But when I go down, I don’t USUALLY eat standard Southern seafood as that’s what I can get up in Tally plus my semi frequent trips to the panhandle, Alabama, Mississippi and Louisiana. If my parents want seafood we usually meet in the “neutral area” of Cedar Key or in Homosassa Springs/Crystal River as there are a ton of great seafood places there (Quick sidenote, if in Apopka the Nauti Lobstah has good southern fried catfish and Yankee/New England seafood dishes). When I’m in the greater Tampa Bay Area, I like to get high quality NYC and Philly “Italian” from snowbird immigrants in Brooksville, Ridge Manor and Spring Hill; grab Greek from Tarpon Springs; or Cuban or German from Tampa. There are some seafood dishes in all of that, but not a “seafood restaurant”.
So far, I haven’t ran into a “seafood restaurant” in Tampa that is equal to or beats the options in Cedar Key, Crystal River/Homosassa, Battleship Row Alabama, Biloxi/Gulfport, 30A, Pensacola, Slidell and of course New Orleans. Frankly even Shell Oyster Bar and some places in Apalachicola/Panacea/Carrabelle beat the places I’ve been to on the coast in Tampa and St Pete (Clearwater and Dunedin have some better options). I especially dislike some of the frequently mentioned older Standby’s like Leverrocks and Oystercatchers as they are too pricey for subpar seafood. Honestly, Tampa, Pinellas Park and St Pete may have the worst seafood in the state no joke As I’ve found restaurants I would unflinchingly recommend everywhere from Pensacola to Jax down to the Keys and in small fishing villages all along the Big Bend down to Pasco County and starting back up again in Sarasota down to Ft Myers PLUS isolated interior Florida places like Apopka, Clewiston, Okeechobee, Dunellon, Ocala etc…
So although that’s a very long winded “No, I don’t know of any quality seafood restaurants in Tampa” (Jax and St Augustine have far more that I like), I can give you a couple of tentative suggestions. My parents and in-laws both like Shells (unrelated to the better Shell Oyster Bar in Tally) which is a former Florida wide chain now shrunk back to the Tampa Bay Area. My opinion is that Shells are better than chains like Red Lobster, Bonefish and Bubba Gump Shrimp, but not on par with dozens if not a hundred places I could name in the rest of FL, GA, AL, MS and LA. I did eat there a lot as a kid and teenager and have stolen their great coconut shrimp dipping sauce recipe (equal portions orange marmalade, Publix brown mustard and pickled horseradish plus some black pepper for extra heat). Catch 23 has some decent Floribbean not standard southern seafood (So nothing to compare to the great places in the Keys and Miami but better than nothing). Skipper’s Smokehouse isn’t a seafood place in any sense of the word but does have some decent seafood in the form of an iconic (maybe even creator) or a Blackened Grouper Reuben sandwich, smoked Gator ribs, alligator and Cobia nuggets, etc…all of which I like better than the seafood I’ve gotten at true “seafood restaurants” in Tampa. It’s even got an almost tolerable raw bar. Big Ray’s Fish Camp is probably the best standard seafood restaurant in town but don’t count that as a giant raving Review from me. Oystercatchers is locally famous for its seafood and nice waterfront views but I only go for the brunch on rare occasions not the overrated seafood. For views and slightly upgraded seafood I’d suggest the Rusty Pelican.
So long story short, gun to my head, can’t eat at an ethnic restaurant that has great seafood like some of the Greek restaurants in Tarpon Springs and it has to be seafood in just Tampa…..I’d probably say go to Skipper’s Smokehouse first even though it’s a hybrid bbq/seafood place, Rusty Pelicon second, Catch 23 third, Big Ray’s Fish Camp fourth, Shells Fifth (it would be the most convenient to get in and out of, just nothing super special) and don’t go to Oystercatchers except for brunch. The Crab Shack just across the Gandy barely into St Pete is pretty decent but not mindblowing for standard Southern Seafood.
As far as seafood markets, keep in mind I haven’t been to one post pandemic but the best in the area that I remember was IC Sharks just off the Gandy barely into St Pete (so near the Crab Shack), but during the pandemic it was forced to move off the bridge itself to a further into St Pete location due to local zoning BS. The new location supposedly has the same quality raw seafood to pick up (I haven’t been to the new location) but no longer carries bait/live shrimp and crabs. The new location does have a little seafood restaurant that on paper and principal should be good but I haven’t been so that’s why no rec from me. Backups for seafood markets if IC Sharks now sucks would be Blue Sea, Captain Mitchell And Cox.
One caveat to all of the above is that Ted Peters in St Pete is an absolute iconic restaurant that should be visited at least once. But it’s known for smoked mullet, mackerel and Amberjack not fried food or fancy Floribbean fare.