First, a few more suggestions about the Smokies.

Above I mentioned the beautiful Cataloochee area and the elk herd. Another area I love to hike in is Big Creek. It has waterfalls, places to swim and in general it's a beautiful hike along a large rushing creek.
Since you will be coming in from Chattanooga, check out the Abrams Creek area for hiking and another lovely waterfall.
For guided hikes, consider:
https://sites.google.com/site/justgetoutdoors/
I haven't hiked with her yet, but I may be doing an excursion led by her later this summer. If I do, I will report back.
As has been noted above, both Gatlinburg and Cherokee are very, very, very touristy and tacky. But if you will be out and about all day and just want cheap accommodations, they could be okay. My recommendation is to find a nice Inn around Townsend if you want to focus on the west side of the Smokies. Since the east side of the Smokies is an easy day trip for me, I don't know much about accommodations on this side, though I am sure there are many lovely Inns and cabins to rent.
I would be wary of driving the Cades Cove Loop. It can be so congested that it basically becomes a long parking. And once you're on it, you are stuck in the traffic.
On the other hand, the Foothills Parkway on the west side of the Smokies is gorgeous and not crowded when I was there. It would be convenient for you, if you come in from Chattanooga.
Like djp98374 I recommend Charleston strongly. If, like you, I had only two days, I would spend them in Charleston, not Savannah. But as a Charleston native, I am a bit prejudiced, of course.
Is there a particular reason you are stopping in Myrtle Beach? It's another very, very touristy city and rather ugly, in my opinion. Charleston or some of the smaller towns on the SC coast would be much more beautiful.
If you are interested in natural excursions on the coast, check out:
http://www.coastalexpeditions.com/
I have been out with them many times on their Bull Island Ferry, and have enjoyed every trip.