I don't know any dart throwers in the area, but Bailey's Sports Grille in the Seven Oaks center (between Kingston Pike and Parkside Drive - no real "anchor" stores in this strip center except a Burlingtons) has darts. Not on the Powell side of town, though. You might check with Lewis - he might know that area better.
You might also try:
Greater Knoxville Darting Assn, PO Box 52128, Knoxville, TN
and a google search brought up this article:
Baileys Pub, Knoxville - Dart Tournament
STEEL DARTS ARE BACK IN KNOXVILLE-WE NEED YOUR SUPPORT!! I know you steel darters are out there-Come to Baileys Pub in West Knoxville Thursday Nights at 7:30 and 4:00 Saturday afternoon. Greg Edwards has put a helluva blind draw and now we are starting an inhouse dart league. Lots of fun. Great Place. Blind draw bringing in 30+ darters. A great time is guarenteed, just like the old days of Bombers. Come and check it out.
and, this Metro Pulse article from the late '90s:
http://weeklywire.com/ww/03-09-98/knox_gamut.html