In Jacksonville check out:
St John's Golf and Country Club - good track, tough.
South Hampton - not as tough as St Johns, but a fun track. Also, it is next door to St John's which can make for a good 36 day. They are close to I-95.
Eagle's Landing - its in Orange Park and a bit of a drive from 95. I liked playing this course. It is not a significant design, but I always had fun and had to hit a lot of different shots.
Bent Creek - this is also out a bit from 95, but is a good muni course. For the price, it was always in good shape and has some good holes.
I don't remember there being much in St Augustiine besides the World Golf Villiage (Slammer & Squire or King & Bear, King & Bear is the better of the two).
Don't play Royal St Augustine. It has a lot of bad quirks and silly holes. I hated it everytime I played it.