It may be hard to define the borders of the Texas Hill Country, but you will know it when you are there.
We always make Fredericksburg our base for visits to the Hill Country. This is one place where we actually prefer the KOA. We have been going there for a good many years and know the spots where we want to stay in the campground. We can visit Luckenbach, Boerne, Llano, Kerrville, LBJ historical sites, Enchanted Rock, and even San Antonio if we wish while staying at the KOA in Fredericksburg.
And yes, Inks Lake State Park is great, but Fredericksburg is better for a hub. Sometimes we move over to Inks Lake for a couple of nights.
By all means, plan your visit for early April to see the bluebonnets in all their glory. Not every year is a really good one, but we usually find some good spots along the Willow City Loop