Jazz Scene in Florida - Tampa Bay, Jacksonville, Pensacola areas

Pensacola is a lovely town in varying states of prosperity and hurricane recovery which blossoms seasonally with snowbirds and loves any kind of party or festival, and live music with generally broad appeal. There is a substantial artist community and numerous galleries. Some solid jazz pianists and singers find most of their work in hotel and resort lounges, just the way it is. The jazz society is variably active depending on leadership and member enthusiasm, and tries to support local schools. Regular free evening concerts in a downtown green space included more Dixieland than bop or hard bop, but those were suspended due to lapsed funding which had been provided by local business and private patrons. Paying gigs must appeal to tourist taste and you find singer-songwriters at the beach bars by day and rock at night. There was a weekly free blues concert on the beach with local bands, don't know if still happening. There had been genuine annual jazz festivals at nearby upscale towns such as Seaside but I don't know their current status. This was my impression as a music consumer who lived there about ten years ago. Not to say you couldn't scare up some players for a jam if you asked around.

I never saw busking anywhere now that you mention it. Don't know if that is an ordinance or lack of talent or lack of audience.
Not to be crass, but Pensacola is in or adjacent to the ******* Riviera and a typical summer tourist on the beach might be deep into a six (12?) pack and playing country on their radio.
Strange to me was fact that peak tourist season was summertime, while the climate greatly favored fall and spring... which is when the snowbirds are in residence. They make the symphony, opera and touring theater productions possible, so maybe more jazz could find an audience. JazzPensacola has web and FB pages--suggest you contact them for current info.
If you are driving, certainly settle in Pensacola for a few days. Lovely hotels on the beach as well as some new hip places downtown. Walk the downtown and galleries, eat at some great restaurants, visit the Naval Aviation Museum. And of course New Orleans is only three hours to the west so you will have stopped there first!