OMG! I remember now! Only you left off the coolest of the railroad terminals and the most Easterly? It was the Atlantic and East Coast Railroad station, AKA: Florida East Coast freight Terminal. I could have been many things including a modern Amtrak or Commuter Rail station.
You can see the terminal in the upper middle section of this image. You can also see the commercial building density of Broad, Davis and Adams Streets in LaVilla. The block of residential structures between the demolished railroad terminal and Adams was the epicenter of the bordello district.

Here's an aerial of this same area today.

Some images I scanned for an article on LaVilla in 2006.

we park on this building's foundation today.



link to full article on LaVilla's destruction:
http://www.metrojacksonville.com/content/view/250/120/