Jazz Festival was well executed and kudos to the organizers. It shows what we can do when we put our talent to work.
Spring (mid-Feb to mid-May) and fall (mid-Oct to mid-Dec) themed festivals of music, entertainment (open up the theaters and museums), food, children's activities, and the arts with a bit of river and fireworks fun mixed in should work well. Tie in with seasonal Jags/college games and Jax Suns games. Close Bay Street, Water Street, Laura Street, Main Street, and the Main street bridge and mimic the Super Bowl festivities. Bus people in from the park'n'ride lots in the burbs like the Jags do on game day and promote the city garages and convention and stadium lots with shuttles. Let the bicycle taxis, horse & buggies, and open-air trams join the mix to move people over a larger festival area.
Need to make sure there are adequate traffic control and security, rest rooms, rain locations, and "cool down" spots so people don't have excuses to not come.
Those are our best times of the year weather-wise as well and the fall festival could be used to boost holiday shopping downtown.