Chris,
The almost-sure spot in the Smokies for finding Swainson's Warbler is
Schoolhouse Gap Trail:
http://ebird.org/ebird/hotspot/L1176932
Get there early and walk the trail in for a few hundred yards and listen for
them. They should be very active right now. They hang out in the
rhododendrons along the trail and be difficult to actually see, but they are
very vocal.
Bates Estabrooks
Anderson County