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!