The Mountain Times is a local publication for Watauga/Avery/Ashe counties and publishes weekly classifieds for rentals. This is the website
Untitled and click on Apartments/Duplexes under Real Estate Rentals and you should see all the current listings. The listings come out on Tuesday of each week although the publication comes out on Thursday. There are several apartment complexes in Boone around ASU (Appalachian State University).
Hope this helps,
Carolyn