We also normally like state parks, but when we were visiting the Asheville area in 2005 we stayed at Mountain Stream RV Park in Marion because we wanted the convenince of full hookups for a week's stay. It had easy access to the Parkway, and was centrally located for the nature stuff, which was more our focus. Their sites are pretty small, but it's a nice well kept park.
Mountain Stream RV Park Home Page
We drove into Asheville one day for the Biltmore House tour, which was amazing. If you go there, it's worth it to pay the extra for the headset audio.