Naked Hiking Day is done anywhere on the Appalachian Trail that you feel comfortable doing it. (I've read that it is illegal in New Hampshire). It is not sanctioned by the AT Club. More people participate in Naked Hiking Day more often in the Virginia stretch of the trail than anywhere else.
I found a pretty lively discussion about it at this address:
http://forums.alpinezone.com/about178-0.html
If you do it, you might want to avoid nudity near trailheads and at trail shelters. June 21st falls on a Tuesday this year, so there won't be as many people on the trail as there would on a Saturday. Hikers who've done it suggest having something handy that you can quickly slip into if you see a ranger or kids approaching you along the path ahead.
A nude couple would probably be perceived as less threatening than a solitary man.
Some parts of the AT get daily rain showers in late June. Be ready for them and the cooler air it brings! And if you are near Mt. Rogers, well, it is often very chilly there because of the elevation.
One hiker recommended fleece lining on the pack harness and hip belt to protect your skin.
