Mt. Sterling should be fun. Spend day one hiking Big Creek trail from Big Creek Ranger Station and stay at Walnut Bottom Campsite. Next night you can ascend up to Mt. Sterling and it has a firetower with a panoramic view of the park from that end. However, you're quite a way from Clingman's Dome from this location. Clingman's Dome is in middle of the park, nowhere near where the AT exits from either end of the park. From the southern end, there probably more panoramic views and is closer to Clingman's than northern end where Mt. Sterling is. I cannot remember the numbers of the campsites from southern end, I'll get back to you on that.