You have many options. You can camp at Elkmont or Smokemont Campgrounds for a fee but you will be near the rivers or right on them. You can camp at Cataloochee and be on that stream. These are developed campgrounds in the Park. Cades Cove is close to some streams. The backcountry offers many opportunities to camp on a stream. They are everywhere in this 1/2 million acre park. Send me an e-mail and I'll send you a free map of the Park. Please include your mailing address. Pineman gave you a link that will probably answer your questions. There is not enough room here to list all of the on-stream backcountry sites. The GSMNP is full of them. You could start with the map or the website and if you have any specific questions call the shop and we will try to answer them. You can get a backcountry permit and camp in any backcountry site in the Park. Permits are available at other locations as well. I have seen very few rangers or people in the backcountry sites that I use. Sometimes we are the only people there. It depends on the time of year of course and the campsite.