At the present time, there are about 30 campgrounds that surround the Smoky Mountains in towns like Gatlinburg, Pigeon Forge, Townsend, and Cherokee. The amenities differ greatly, but generally offer a great place to park your RV during your stay often for less money than a motel room. I have posted a link below with more detailed information on these Campgrounds.
There are currently 10 sites in the front country inside the national park boundary. You can set up a tent or park your RV in these sites. There are restrooms and running water (cold) at each. The months of operation vary, so you will want to check and make sure the one you want to visit will be open during your stay. Costs start at $14 and go up to $30 at the time of this writing. Some fill up quickly and reservations are recommended well in advance. There is a link below to the Park Service who handles the reservations.
BACKCOUNTRY SHELTERS AND CAMPSITES
Staying anywhere in the backcountry requires a permit. Some shelters and campsites are “rationed” and you will need to make reservations well in advance. Others can be reserved much closer to when you depart. This used to be free, but the fee is now $4.00 per person per day. You also cannot stay more than three consecutive nights. For further information, I have placed a link below to the reservation system.