The most accessible and public area for bouldering is Honey Run. It is linked in the margin through Knox county parks site. This area is undeveloped and I really encourage anyone who checks it out to be respectful of the park rules as well as other visitors just there to enjoy the waterfall. This is a beautiful site and deserves being enjoyed in a respectful way. Please stay on the trails and take out what you bring in. Email me for any more information!
Enjoy! John

