Greenbrier is indeed part of the SMNP. It's off of 321 just east of Gatlinburg. BTW, Pigeon Forge is a lot uglier than Gatlinburg. Townsend has the closest motels to Cades Cove. You can camp right outside of the cove while in the park. The dirt roads will get you far from the crowds. Rich Mountain, Cherokee Orchard/Roaring Fork, Heintooga/Round Bottom Road and Parsons Branch. Parsons branch may still be closed for repair. Use the two dirt road short cuts in Cades Cove to avoid the traffic after you scope out the area. Anytime after 10 AM and your screwed. Pick up the map of auto tours through the park at the visitor centers. Avoid the weekends during leaf season.
I gave a further rundown over on APUG page 12, geographic location under photobum.