Great Smoky Mountains National Park

Go too web site mypigeonforge

There are a lot of hikes so I think you have to pick based on your capability.
I do suggest Cades Cove.
The motor trail behind G'burg.
Be sure to visit Elkmont.
Do a sunset at New Found Gap or Clingmans Dome

Beware that April 22-29 is the Wildflower Pilgrimage week, and things may be more crowded than you would expect that time of year. Reservations would be a good idea.

Drive the Cades Cove Loop. Start early and along the way, hike the 5 miles round trip to Abrams Falls. Easy trail.
Drive the Roaring Fork road and hike the moderate 5.4 mile round trip hike to Rainbow Falls.
Also, The Trillium Gap Trail leads to the 25-foot high Grotto Falls.

There is so much to do in the whole area. One hidden gem is Forbidden Caverns if you would like to see a cave. Its close by the Bush Bean factory for a good lunch and a quick tour through their little museum. There is a good aviation museum at the Sevierville airport too. Not a lot of aircraft on display but they do have 3 P-40's. The museum itself is interesting.

G'burg has the Ripley's aquarium and other Ripley attractions and its downtown area is very walkable. Pigeon Forge has Dolly's Stampede, a great dinner show and there is a Titanic exhibit that is worthy of a look.

If you are inclined for a casino fix then there is Harrah's in Cherokee NC just over the mountain. In Cherokee there is the Museum of the Cherokee Indian and not much further down the road is the Wheels Through Time museum in Maggie Valley. Easy day trips.

If you have never been to the Biltmore Estate in Asheville take a day to go. Asheville is an hour away, another easy day trip. Unless you are a hiker there is not a whole lot to do in the park itself. You have lots of research to do.

Pancake Pantry on main street in GBURG for breakfast and/or lunch.

As others have said, don't miss Cades Cove. If you hike, there are some great trails there such as Abrams Falls (already mentioned) and Rich Mountain Loop. Outside of Cades Cove, Cucumber Gap Loop is a nice hike, as is Rainbow Falls, Clingman's Dome, Andrew's Bald and more. There is a lot to see around the Cades Cove visitor center as well as around the Oconaluftee Visitor Center. The Sugarlands Visitor center has a nice nature trail behind it. Alum Cave trail is nice as well. There is more to do than you can fit in a week, so I'd probably concentrate first on Cades Cove then Clingman's Dome as well as Newfound Gap Road.