Just east of Asheville is Asheville East KOA in Swannanoa, NC. Recommend this for your stop. Friendly campground, laundry, full hookups, creek & lake. Grocery store/restaurants minutes away. Easy access to KOA from I 40 (Swannanoa exit).
Same exit has Mama Gerties which is a nice campground but requires you drive up a fairly steep slope to sites that would accomodate you.
Edit: forgot to mention both are dog friendly, KOA has a small enclosed fenced area where dog can be off leash. Large enough for our Aussie to enjoy off leash.