June can be a funky time as many local golf courses do a heavy aerification and top-dressing just after Memorial Day.
Top courses in the area to consider include:
Ponte Vedra Inn & Club - Ocean Course
Pablo Creek Club
Timuquana Country Club
Sawgrass Country Club
Plantation at Ponte Vedra
King & Bear at World Golf Village (in St Augustine)
(each of the above I place ahead of the Valley Course at TPC)
If you're up for driving south 45 minutes the Ocean Course at Hammock Beach is worth it.
Drop a note and I'd be happy to help further.