Definitely do this. Cades Cove is typically a traffic jam of tourists in the summer, but the Saturday/Wednesday ride is wonderful.
Random thoughts:
The Laurel Falls hike is popular with families because it’s short and paved. The same with Look Rock on the Foothills Parkway in Townsend (lots of overlooks, too). If you want to try your endurance, ride your bike over the Parkway.
The views from Chimney Tops is great, but it’s a strenuous hike.
If you like twisty roads and motorcycles, take a ride on 129-The Dragon to Deals Gap. It’s got over 300 curves in 11 miles.
The Tuckaleechee Caves are a good way to cool off. Same with tubing on the Little River.
The Smokies minor league baseball is close by. They do lots of events at their games like fireworks, bands, giveaways and such.
Pigeon Forge is full of ridiculously tacky touristy things. Go cart tracks, helicopter rides and dinner theaters (Lumberjack Feud, Hatfield & McCoys, Dixie Stampede, some bible thing). There’s even a replica of the Titanic for some reason. Of course Gatlinburg is just down the road. These areas do get extremely crowded, so be prepared!
There’s a cool alpine coaster just outside of town, along with zipline tours.
Knoxville is very close by if you want to hit some bars or restaurants. Just head to Market Square and walk around. They also have an okay zoo. That week they’re doing a Brewfest, Pridefest, and Slide the City.
There’s some great mountain biking at Knoxville Urban Wilderness and Haw Ridge Park.
Urban Wilderness
Haw Ridge
Alpine Coaster
Cades Cove
Laurel Falls
Look Rock
Chimney Tops
The Dragon
Tuckaleechee Caverns
Tubing
Smokies Baseball
Brewfest
PrideFest
Slide the City
Let me know if you need more info on a specific topic. I’ll post more ideas as I think of them.