Do you have a preference on what side of the lake you are on? Are you going for anything specific of just to visit? Norris covers a lot of ground, and there are different things to do and see at different spots. I agree with Cove Lake State Park, it is a nice place and convenient to the lake.
Our camping club has an upcoming event at Cove Lake CG in September. It's a TN State Park.
Friends of ours use Big Ridge because it's close to home, but they don't really recommend it, said the sites just weren't up to par with Cove Lake.
I can't recommend either of them since I have never been, but I do know that Norris Lake is beautiful. There are several other TVA lakes within 100 miles of Norris. (Cherokee, Boone, South Holston, Watauga)
I don't really have any insight, just wanted to add that we are going there in a couple of weeks and have reservations at Big Ridge State Park http://tnstateparks.com/parks/about/big-ridge
We weren't looking for a big "resort" type place so this will hopefully serve our needs. I'll let you know.
I lived in LaFollette for a few years back before Norris lake surounding property became do developed. There is a beautifull camp ground close by called Cove lake State Park, on Highway 25 just south of Jacksborro,
We stayed on Norris Lake for a couple of nights 25-30 years ago with our boat. At the time they had "floating cabins" at most of the marinas. We there looking to buy a lot or possibly one of the "cabins", then found out there were no waste facilities for the "cabins", waste dumped into the bottom of the lake through long hoses. Left after finding that out and never returned. Our favorite was always Dale Hollow Lake NW of Norris Lake, big, deep with clear water, unless heavy spring runoff. We stayed at Obey River COE Park for years, easy access, nice dock restaurant with in a 1/2 mile. Probably closer for you being from Louisiana.
We stayed at Mountain Lake Marina and CG for a while. The sites could be a bit bigger but most of the sites have new services installed. The CG is on the west side of the lake east of Rocky Top off of I-75. Norris is a pretty steep sided lake and this CG will tire you out walking back from the lake if you are near the office. Randy p.s. If you are there during football season you may get a visit from Lucy the dog. She feels ignored at home (she lives at a neighboring house) on Saturdays and comes over and visits the campers.
We had a friend that had a houseboat that was moored on the lake and we visited him there several times a few years back. The lake is big and beautiful with lots of wildlife around the shoreline. Don't know much about places to stay since we stayed in the houseboat.