Ed,
Be sure to pick up a copy of the Golfer's Guide in any of the local markets and convenient stores. Plenty of coupons inside with listings for all of the public and resort courses in the area. My rec is to try either Old South (value) or the Hills course at Palmetto Dunes (not your typical flat low country course. Hills designed some ripples in the fairways). I also like John Conley's rec of the Cupp at P Hall, but I haven't been in several years. It's a fun golf course with a look unlike any other (designed on a computer with lots of linear features).
Of course architecturally, Harbour Town would be the one to see, but it has always been pretty expensive to play it. They are running twilight specials now however. This summer the twilight rate is I believe $135 after 4PM. Still a lot, but not the $225+ it used to be year round.
I think the Palmetto Dunes courses are in the $55 range in the afternoon this summer and Old South, even less.
Have fun! Hope you're well!