I've been doing the BRP for several years in October with another couple. We decided to start at the top at MM (mile marker) 0 and head south to the end. This will take a few years to complete. I love the Asheville area. Obviously Biltmore Estate is a sight to see for the house as well as the garderns. Black Mountain just north of Asheville is quite an artist community as Asheville has become more affluent.
For the BRP, I'd suggest to head south at least to the Devil's Courthouse at MM 422. It is a fairly steep hike, but great view. You will have passed
Looking Glass Falls,
Looking Glass Rock and Graveyard Fields on the way. These are worth a stop and looksy.
Graveyard Fields should have some great colors.
If you have time, take Highway 276 (near Cold Mountain.... yep, the movie) to Brevard (home of the
white squirrel) and find Dupont State Forest in Transyvania County. You will have three great falls to view on the trail...
High Falls,
Triple Falls and
Hooker Falls. All three plus Bridal Veil Falls further down, were featured in the film the Last of the Mohicans. This can be a good day hike and the best tip is to have two cars. Park one at the bottom (Hooker Falls) and start the hike from the top (High Falls). Go retrieve the car at the top now.
Keep in mind that the weekends during this time of the year, BRP gets congested. Leave early, stay late and bring plenty of patience. Bring lunch, liquids and snacks. There are plenty of places to pull over and have a bite. A spread to sit on isn't a bad idea either.
Have fun.
EDIT:
A good book for hiking trails and waterfalls is North Carolina Waterfalls, A Hiking and Photography Guide by Kevin Adams