There are a couple of places that deserve the title "Harlem of the South", and LaVilla certainly has a place along with Miami's Colored Town/Overtown, Richmond's Jackson Ward, and Memphis's Beale Street area.
As Lakelander says, one of the differences with Jacksonville (and to an extent Miami) from other Southern cities with black enclaves was that the wider community was comparatively more tolerant, or rather, comparatively less intolerant, toward its black citizens for some time after Reconstruction. This was heavily influenced by local business interests, who relied on Northern investment, connections and tourism. The erosion of mobility and agency for African-Americans in places like LaVilla in the early 20th century led many of the best and brightest to move to Harlem, where they created a Renaissance. When people like James Weldon Johnson and Zora Neale Hurston came from Jacksonville, it's no stretch to call it the Harlem of the South.