Not convinced FSJ is the best or preferred site. The downtown campus is, effectively, a commuter school so those parking lots are essential for its students. Not like we have great mass transit to get them there otherwise. I also hear they may have a master/long range plan for their needs that may require more intense use of their holdings over time. Regardless, as Jax's population grows, they need to have room to grow with it.
Already discussed here is the former JEA tower complex. Gateway has now said they also have interest. With all the empty or underused real estate in the core, the closer UF is to the center of it, the better for downtown, IMHO. State & Union, in their present state, are physical barriers for students to deal with to access downtown.
An additional caveat: My experience with urban/town campuses, is students won't leave the comfort of their campus environment very much to begin with. Maybe due to all there needs met on or close to campus, a feeling of security, living in the college "bubble" with their social peers, laziness to walk farther distances, lack of interest in the "real world" outside of campus, lack of familiarity with the off campus world... Admittedly, graduate students might interact a bit more, but maybe not as much as some would expect for the above reasons.