I do it two ways. First I simply go the website of the closest town to where I want to stay. I then click Lodging. Not only do the motels, and things come up. But campgrounds as well. Go to their websites, and check them out.
Another way is to go to the State RV website. Like in NC. It is North Carolina RV Parks, and Campgrounds. On that site, The different regions of the state are broken down, and the Campgrounds, and Parks are listed, along with their websites.
All you have to do is. In Google. punch in the state, then Campground. Example. Tennessee Campgrounds. The search engine does the rest.