There are eight elementary/middle schools in Watauga County and one high school (Bethel, Blowing Rock, Cove Creek, Green Valley, Hardin Park, Mabel, Parkway, and Valle Crucis). Hardin Park is actually the only school district that is truly Boone. The others are a little further out. As Kim said below, you can search our MLS using the school districts. You can use our website to search by clicking on search MLS:
As far as recommending neighborhoods, it will completely depend on your price range. If you would like to discuss this further, please contact me. The MLS would be a good place to start though.
Here is the website for Watauga County Schools if you need more information: http://www.watauga.k12.nc.us/
If someone is using REALTOR.com or a similar site to search property, it is not very compatible. Your best bet is to use a real estate website (may I recommend wwwcoldwellbankerblair.com?) and use the advanced research features for an MLS search, and it will show detailed parameters that you can select from, including schools.
Hope this helps - feel free to contact me directly if you have additional questions.