I lived there for ten years and have some lesser known ideas.
Late May/early June is firefly time. Most people go to the Sugarlands ranger station to park and take a shuttle in, but you don't need to. A little before dark go to the Chimneys picnic area on the west prong (this is the actual name of the place, it is located on 441, the main road through the park), park along the road since the picnic area shuts the gate, make sure you have a red tinted flashlight so you don't mess up everyone's eyes. Walk in and find a place to sit and wait until about 30 minutes after dark. There will be literally millions of fireflies and they start synchronizing and flashing in waves. Its one of the coolest things I have ever seen. There will be bears everywhere. Don't feed them or they will hurt you.
I recommend swimming at midnight hole. On the pigeon river at the top of the smokies at the top parking lot where the rafts put in there is a little road that heads up big creek. Go all the way to the top of big creek road and there is a trail that continues on. About a mile up there is the coolest swimming hole with a waterfall pouring in. Water is cold, but it is great. You can jump off the rocks, etc.
There is a similar swimming hole at boxcar falls on the north fork of the french broad. The pool at the bottom is really deep and there is an entire railroad car down in there that fell in from above. Also on the Asheville side you have sliding rock near looking glass. Cool natural rock slide into a nice swimming hole. Looking glass is a great hike. 700 foot cliff.
Cades Cove in not over-rated. On wednesday mornings no cars are allowed and you can do the circle on your bike. Its around 12 miles, super easy. If you are mountain bikers then I recommend the dirty south in Knoxville. It is 5-6 different MTB parks that have been linked together into a 25ish mile loop. They also built a downhill course there. Windrock mountain has full on downhill if that is your bag. Windrock is hard, little easier than Keystone and Winter Park, but not much.
Rafting the Ocoee is great, Pigeon is ok, and French Broad or Nantahala is boring.
Max Patch is a great hike just north of the park. Skip Abrahms falls trail, totally over-rated. Ramsey cascades is OK, Alum Cave and Charlie's Bunion are really good trails. Really the best hiking is on the plateau and around Wilson Creek instead of the park. Best hike in TN is probably the honey creek loop in the Big South Fork. It can be scary though, it has ladders and one is about 70-80 feet up. I REALLY recommend that hike. There is some stuff around the piney river in Spring City that is also really really good and I love the Laurel Snow pocket wilderness near Chattanooga. Lots of hiking out there.
Honey creek
https://www.alltrails.com/trail/us/tennessee/honey-creek-loop/photosLast thing, I don't think you need to avoid Gatlinburg and Pigeon Forge. Yes it is a lot of pancakes, putt-putt, and go-karts, but sometimes that stuff is fun. And Dollywood is a great amusement park.