Brevard is in Transylvania County and is home to numerous beautiful waterfalls. We were in that area a few years ago. The best thing I can recommend is to go to this website: www.visitwaterfalls.com
Across top of the page, check out 'Plan Visit' to get an idea of what to see/do in Brevard. Then click on 'Outdoors' and select 'Waterfalls' to read about and see some of the waterfalls....at the bottom of that page, you can download a map of all their locations.
We were staying in Maggie Valley, but took some day trips to the Brevard area, so I am not familiar with RV parks there, but I feel sure the website has some listed.
You are near Cold Mountain, scene of the book and movie of that name.