I enjoyed a week's vacation at Nantahala Lake in late June.
For pure pavement riding, there are a few options. Wayah Road has long climbs and some swooping descents. Junaluska Road toward Andrews is straighter, but still plenty steep in spots.
If you have a bike that can handle pavement AND dirt, you'll be in heaven. Here are some of my favorite routes:
-Wayah Road to the top of Wayah Bald. The last six or seven miles to the top is a dirt forest service road. A groovy grinding climb through a beautiful forest on the way up and a ton of fun on the way down.
-711 Loop. 711 is a paved forest service road, but it was last patched and maintained during the Nixon administration. (You may think I'm exaggerating, but wait 'til you see it!) Big climbs, tons of wildflowers this time of year, and very, very little traffic. Loop back around via Wayah Road and you'll see some nice lakeside.
-Winding Stairs Loop. Ride Wayah Road all the way down to US 74. This road follows the Nantahala River past tons of cascades and is a blast to ride. A nice greenway follows the river to Winding Stairs Road, a forest service road that climbs back up out of the gorge. Winding Stairs is dirt. It does wind a bit, which I think makes climbing a lot more fun, because you can look down on where you've been. On the top, past pretty Queen's Lake, the pavement begins again, and there is a wide open descent back to Wayah Road.
-Old River Road. This is a forest service road along the Nantahala between Junaluska Road and Wayah Road. It's pretty flat and fairly smooth for a dirt road, with lots of nice cascades along the way.
At the time of my visit, most of the dirt roads were pretty smooth and might be do-able on a road bike with some tough tires.