I know a good place, altho you may have been there since you live here. But husband and I used to take our dog with us to the Carl Sandburg Home in Flat Rock, just south of Hendersonville, as you probably know. Call ahead to make sure it's open. Walking all around that property will wear you slam out!
You pull off in a parking area, it's a State Historical Site, and just as you go thru the entrance gate, there's a little lake in the woods to the left, and folks walk their dogs around it all the time. We then walked up the dirt road to the house. While husband held onto dog, I went inside, but I left before the tour was over, after I saw Sandburg's working library area. We went around the left side of the house (as you face it), behind there and up a somewhat steep little trail, and talk about some BIG flat rocks up in those woods behind the house! We clammered around up there, and then cut over to a little country road that came out along the right of the house (as you face it), and wound up at the goat barn area across from the house, the dog enjoyed seeing his first goats in the herd in the pastures there.