Franklin, NC to Nantahala Outdoor Center (near Wesser, NC) is 27 miles with some decent climbs and great views from Siler Bald and Wayah Bald. The trip ends right at the original NOC with plenty of rafting opportunities.
Ron Haven, owner of Franklin's Budget Inn, offers a hiker rate for rooms and will shuttle your vehicle up to NOC and you back to the AT trailhead near Franklin for ~$50-60. It would be a scenic trip with a classic float at the end.
Or you could hike from Fontana Dam (south edge of the Smokies) south to NOC. Again 27 miles, though the climbs are steeper with less views.
The Hike Inn would be available for shuttles.
Another decent option would be Davenport Gap (north edge of the Smokies) north to Hot Springs, NC, about 36 miles. There are a number of outfitters in town and just outside of town running raft trips on the French Broad River. Plus, you get the experience of finishing with a classic trail town. Curtis Owen of
Standing Bear Farm and Hostel again will provide lodging and shuttle services. He tends to charge less than others on the trail corridor. The e-mail listed is no good, but you can reach him by calling the phone number on the webpage in the evenings. Standing bear is located about two miles from Davenport Gap.
These are the areas I know well regionally (and I have rafted with NOC on both the Nantahala and French Broad), and businesses I have had good experiences with. If you have any other questions, let me know.