Pablo, if you have access, would be at the top of the list.
Others - all worthwhile (some private) would include:
TPC Valley, Timuquana, Deerwood, San Jose, Ponte Vedra Ocean... Of those - Ponte Vedra (as a resort guest) and TPC Valley are accessible to the public.
South of town - Palencia is private (Art Hills) and gets mixed reviews, King & Bear and Slammer & Squire at World Golf Village are fine resort courses, and St Johns G&CC is a fine public-access course.
North of town - Amelia National is an excellent new private Fazio course, North Hampton is an interesting publc-access course, and the courses at Amelia Island Plantation are resort courses.