I am a native of South Georgia and have played literally hundreds of rounds at all of the Jekyll/Sea Island/Brunswick courses - and others nearby.
1. Be prepared to drop some real dough if you head over to play at Sea Island. I agree that Seaside is really, really (REALLY!) good, but it comes at a price.
2. The Great Dunes course is SO WORTH IT. The first six holes are magnificent, and the others aren't bad. If the state just put a little bit of money into a renovation, this could be a museum-quality golf course. The little tiny round greens are just a shame. But play it (maybe a couple of times).
3. I agree that Oleander and Pine Lakes are the best of the three 18-hole layouts. Oleander was once the site of final-stage PGA TOUR qualifying.
4. Brunswick CC - yes, Yes, YES! Play it for sure. The work that Love's team did down there is outstanding. Great day of golf at BCC!
5. Just down I-95 in scenic St. Mary's GA (that's where you catch the ferry to go to Cumberland Island, which is a side trip you may want to consider - absolutely beautiful) is Osprey Cove GC. Nice little Mark McCumber course. Hidden gem status and site of several GSGA championships.
6. My hometown of Waycross, GA is about an hour inland from Jekyll. Okefenokee CC, where I maintain a non-resident membership to this day, is yet another Joe Lee design BUT is built on incredible sandy soil on the banks of the Satilla River (which actually comes into play on a couple of holes). There is a good 40 feet or so of elevation on this course - rare in coastal Georgia. IMO, it showcases the best that Joe Lee could do. Very good. I think it's worth the drive. Side note: I got hooked on GCA by spending many an afternoon with Gentelman Joe and his associate Rocky Rocquemore during construction of Okefenokee. I was completely absorbed in golf at the time, a 13-year-old who wanted to know how ALL of it worked. And they were willing to let me tag along.
Obviously explore Millionaire's Village on Jekyll Island. The oaks with their spanish moss - just gorgeous. Fort Frederica on Saint Simons is a fascinating piece of colonial history. Again, Cumberland is one of the great wild places.
Enjoy! PM me your email, and I'll send you a story I wrote on the Golden Isles for Colorado AvidGolfer magazine.