Well.. east is not an option.
Pawleys Island is famous for the Pawleys Island Hammock.
There is a new federal prison up around Kingstree. I don't know if they give tours.
Really not much to see.
If it were me, I'd probably head down 17 to McClellanville and to to the shrimp boat docks. They have a seafood store there where last year you could get fresh local shrimp (make sure you ask for local shrimp) for $5 a pound. I'd maybe get 4-5 pounds of that in the cooler then halfway between McClellanville and Awendaw is a federal campground that is on the intercoastal waterway Buck Hall Buck Hall Recreation Area
I'd spend the night there and gorge myself on shrimp. There is a store for provisioning just the other side of Awendaw, the Sewee Outpost. They have a great selection of food and other stuff there Sewee Outpost | Your Low "Country" Store
Right down the road from the Sewee Outpost there is the Birds of Prey Center. They do daily shows or exibitions or what-not. The Avian Conservation Center and The Center for Birds of Prey | Plan Your Visit
Also in Awendaw is the Bull Island Ferry which is a ferry ride (no cars) out to Bull Island Bull Island Ferry-Cape Romain National Wildlife Refuge- Mount Pleasant, SC - Attraction - in South Carolina
Thats pretty nice.
All of this is within easy driving distance of Buck Hall.. just down Hwy 17.
Oh, also in Awendaw, across from the Outpost is Seewee Restaurant. Fried pickles are the local favorite.