Climbworks Canopy Tours--make reservations
Parrot Mountain
Hiking in Smokey's
My nephew loved Zorb, I didn't attempt it.

Perhaps a trip over to Ashville to see The Biltmore

I like Tomatohead for a meal in Knoxville(on the way in or out of the area)
Cakes By Bakin Bishop is good and Kilwin's Ice Cream are both good for a stop for something sweet.

What made you interested in those places? It's hard to give input without knowing anything about your interests.

Country Music Hall of Fame
Ryman Auditorium
Hermitage
Parthenon
Grand Ole Opry Show & backstage tour
Belle Meade Plantation
Tennessee State Museum

Great Smokey Mountains National Park
Arts & Crafts Loop

Thanks for the replies. We will look into them all. As for why, we went to Hawaii last year and were looking for a place to drive and save airfare. We like country music, so Nashville seemed like a spot, but we didn't think we'd be busy enough for a whole week, that's where Dollywood came into play.

For Nashville, if you're a country fan I'd add to abram's (good!) list the Station Inn - it looks like a complete dive (and it is), but it's where you're likely to find some of the most true country/bluegrass around. The honky-tonks downtown will have musicians, more along the lines of what you'd hear on the radio.

The Bluebird Cafe is one of the most well-known venues in town; it's not strictly country, but features singer/songwriters, many of whom have written a lot of country songs. It's different from other places around because they really enforce quiet during the music - no phones, no chit-chatting during songs. If you plan to go there, book tickets early - it's been selling out more than usual because it's featured on the show Nashville.

Loveless Cafe in Nashville

Las Paletas for popsicles(yeah, they are that good)in Nashville

The Hermitage (Andrew Jackson Home)

Thanks for the responses. We are currently debating whether to shorten our time by a day at each stop and spend a few days in Charlotte. Any thoughts on that?

I think you will need 3 or 4 days at each spot, depending on what all you want to see and do. So, if just a week, then I don't think you would have time to add an additional stop.