I was in FL back in September and spoke with various LEO. WITH a permit, like "Kimber" said, you can have it in a case, shoe box, center console, glove box, etc. or on your person as long as the firearm is "concealed". The firearm is considered "concealed" if it cannot be seen by the casual observer. Holstered between the seats is not o.k., however if you have it holstered between the seats and have a towel, ball cap, etc. covering it from plain sight, then that would be "concealed". Be careful that a gust of wind doesn't cause the towel, ball cap, etc. from getting you into trouble. WITHOUT a permit, you can do the same with the exception of carrying anywhere on your person. Carrying in a purse, fanny pack, etc. would be considered "on your person", so be careful.
gf