Along I-75 and I-40, I can't think of any place to stop and go to the bathroom. The rest areas along those two interstates are nice. However, they're below the mountains, and you don't get the views.
I hope you realize the Great Smokey Mountain National Park is a ways off of the expressway. And to get a good feel for the park, you'll have to drive through it. Probably from Gatlinburg, TN to Cherokee, NC. Both are a good half hour to 45 minutes off of the expressway. And the drive through the park itself is at least an hour if you go straight through the park. Worth it, but allow the time.
I have a suggestion, if you want to experience mountains without the time. It's a slightly different route that's only about 15 to 30 minutes longer....the Cumberland Gap Parkway (US 25E). It runs from Corbin Kentucky (exit 29 on I 75), to Newport, TN (I think exit 435 on I-40), a distance of a little over 100 miles. Although you can cut off in Morristown, TN, and take I-81 to I-40.
It's four lane highway all the way through with a few stop lights, mostly in Corbin, Middlesboro and Morristown. 55 MPH for most of the drive. And the mountain scenes are beautiful.
You'll pass right a couple of parks with beautiful mountain views. The first is the Pine Mountain State Park, right outside of Pineville, KY. It's about five miles off of the highway up a winding mountain road. But once you get up to the top, there is a lodge/picnic area with bathrooms, restaurants and a nice, scenic, mountain view.
The second is the Cumberland Cap National Park on the Kentucky/Tennessee border. You can stop, picnic, go to the bathroom, and hike up to some beautiful mountain scenery.
About 15 miles further down the road (make sure you turn left to continue on US 25E in Tazewell), you'll come upon Clinch Mountain. Nice, easy ride up the mountain. And at the top, there is a small parking lot where you can stop and enjoy the view of the valley below.
I'd take this over the overlong drive through the Smokey Mountain Park. PM me if you have any questions. We take this way all the time to visit my in-laws in Granger County, TN.