There are also several beautiful plantations in the area and the Audobon National Swamp (which is right next to a plantation). There's an aquarium in Charleston that is nice, and even little kids like taking the carriage tour, which I highly recommend if you go to Charleston--it's gossipy and fun.
Charleston is only 20 miles from Kaiwah, but it seems a lot longer because of the roads you have to take to get there. I do love the stretch of Main Road between Johns Island and Kiawah, though; those oak trees dripping with Spanish moss making a canopy over the road are always my sign that I'm back.
Kiawah does not attract the spring break crowd. Neither does Seabrook. The kids hang out on Wild Dunes and Isle of Palms, which cater to singles.
But I've been there in May and it really isn't very warm most years.