Roger,
I make it down to Kiawah a fair amount as my in-laws have a place on the island. If you've never been you will certainly enjoy yourself. In addition to the golf, I would make a point to spend some time in Charleston which is an incredible city and one of my favorite places anywhere. If you want a few recommendations on places to go downtown let me know.
As for the golf on and near the island, here is what I would recommend:
The Ocean Course is the best of any of the courses in or around Charleston. Sounds like you have one round already set up, but if you can manage a replay I would try to do that. Personally, I would play an extra round at TOC at the expense of a round at any of the other public resort courses.
Of the public, non Ocean Course, courses, I think I like Cougar Point (Gary Player) the best. All of the courses there are essentially residential courses, with homes lining the holes, but I find Cougar Point to be the most interesting of the bunch. Turtle Point and Osprey Point are fine courses, but can get expensive if not included in some sort of package deal with the hotel.
Sounds like you're set up with a round at Cassique at the Kiawah Island Club. I really like Cassique a lot and I enjoy it more and more each time I play it. There are some great holes there and I think you'll enjoy it alot. I like it a little better than The River Course (which I think is closed now for renovations, anyway).
Both Yeamans and CC of Charleston are worth a round if you can get access. Neither are really all that far from the Sanctuary (maybe an hour door to door), and I would play at either over any of the daily resort options on the island (not including TOC).
You might want to inquire about Briar's Creek, which is just off the island and is a private Rees Jones course. It's a pretty neat, low-key, experience and I think the golf course is pretty solid.
Also, a fun option is also "The Muni" in Charleston. It's only ~$20 but it is a lot of fun and a total throwback. Some say that Raynor helped design a bunch of the holes when in town building Yeamans and the CC. If you want to squeeze in an extra round at a low cost, it's not a terrible option. It's a fun low country golf course.
Hopefully that helps.