The campgrounds within the Great Smoky Mountains National Park are nice but like campgrounds in most all the National Parks, have no hookups. There are numerous commercial RV parks in the area, mostly in Townsend, Pigeon Forge or Sevierville - - and a few in Gatlinburg close to the park. Generally the closer you are to the park the more expensive the RV parks are.
There are numerous hiking trails and waterfalls to visit within GSMNP, as well as Newfound Gap at the TN/NC state line and Clingman's Dome, the highest point in the U.S. east of the Mississippi. One of your 1st stops should be at the Sugarlands Visitor Center just inside the park, a couple of miles from Gatlinburg. There you can pick up a free newspaper ("Smokies Guide") that has a map of the park and much information about the park including information on Ranger led hikes.
Lots of attractions for the kids, mostly in Pigeon Forge and scores of great restaurants in the area to eat at.