June is good for me, or July, August... I'll be working in NC in a few weeks and the Dragon is only 3 hours away.
I checked the TOD website today and the road is open from 8am to 8pm from the NC side:
ROCK SLIDE UPDATE April 16, 2010: The rock slide on US 129 is located between the Dragon and Happy Valley Road/Foothills Parkway. TDOT has announced in a press release that the 11 mile section known as the Tail of the Dragon will be open from 8 am to 8 pm beginning Monday April 12, 2010. The only access is from North Carolina US 129. THP announced that there will be zero tolerance for traffic violations, so I'd travel the Tail with extreme caution. Please obey the traffic laws and report any undue harassment to us.
Her's a link to a TDOT camera of the rock slide site.
http://earthcam.com/clients/tennessseedot/