GSMNP is a great place to visit. Lots of stuff to do, and previous posters already gave you nice tips. Just a few more:
- The National Park campgrounds are strictly dry camping (no W/E or sewage). They are in beautiful settings, next to the road, but no services at all. Except for the summer months (June through August) reservations are not a must.
- If you are comfortable towing in mountainous, narrow, curvy roads, tunnels and bridges should not be a big concern for towing your trailers. Just take it easy and slow. There are plenty of lookouts to stop and enjoy along the way
- If you need cell phone reception, it will be iffy in a lot of places, so plan accordingly
- Lots of nice trails to hike right of the campgrounds at Elkmont, Julian Price, Linville Falls
- Morning fog can be expected in the Spring. Again, just plan for it and it will be fine.
Enjoy your trip !