The Tampa Bay History Center tells the story of the Tampa Bay region with more honesty and engagement than you might expect from a civic museum. The permanent collection covers a wide sweep: the indigenous peoples of the bay area (Tocobaga and Calusa), Spanish colonial contact and conflict, the development of the cattle and cigar industries, Prohibition-era bootlegging, and the modern port economy.
The exhibit on Ybor City's cigar workers is particularly good, with original machinery, photographs, and recordings of the lectores — the readers who read aloud to cigar rollers during working hours. The Native American gallery has excellent artefacts and manages to give the pre-contact world a sense of real complexity rather than the usual generic treatment.
The building sits on the Riverwalk waterfront, adjacent to the Convention Centre and close to the Florida Aquarium. It can be combined with a visit to the aquarium in a full day out. Allow two to three hours. Admission is moderate and the museum is well worth it — genuinely informative and better-designed than most of its type.