Here's a recent thread with lots of ideas -
http://www.fodors.com/community/united-states/mid-march-family-trip-to-eastern-tennessee.cfm

And at the end a trip report. I'm cutting and pasting that here -
Kristinesonja on Mar 18, 11 at 7:00pm trip report...........Got back last night for our 6 days in Townsend. Had an awesome trip. Flew into Knoxville, easy airport to navigate. The Townsend rental was perfect for us. Love being able to reside so close to the entrance of the park. We loved the house. (http://www.vrbo.com/344471) Clean, comfy, awesome! PERFECT location for us as our goal was to spend time in the park and enjoy nature. We loved staying right outside the Park without the chaos fo PF or Gburg. We spent time with Foot Hills Parkway, hikes along the falls up past Tremont Inst, Dave Crocett horseback riding, Tucaleechee Caverns on opening day, Townsend Heritage Center, hiked Abrams Falls in Cades Cove, Sugarlands Center, hikes at CHimney Tops area, picnics everyday along streams in the park, evening in PF, drive up the New FOund Gap Road to the clouds, a hike on Appalachian Trail, Roaring Fork Nature Trail, evening in Gburg, more horseback riding in Cades Cove, Ober Gatlingburg tram to top of mountain and ice skating. Great vacay!! Nice weather, didn't rain as they predicted. Awesome trip. Love being in Townsend with small 1 trafficlight town and no crowds. Great to expose my FL kids to mountains and new scenery. They hiked like pros and enjoyed it all!

For fishing go to Cherokee and get a license to fish on the Indian Reservation. It is right on the edge of the GSMNP also so you could drive into the Park and go hiking or do other things. you might spend a night or two in cherokee (about 3 hours from Charlotte), and then go on further west to the Nantahala Outdoor Center if you wanted to raft. There is also an entrance to the Park on that side that has good tubing opportunities.

www.blueridgeparkway.org

stay on this scenic parkway and

stay at cute neat BBs along your way.

Rafting and tubing are high on our list...what kind of weather can we expect the 2nd week in June? crowds?

Can't really say, but the areas are large in any case. Weather will be warm in the mountains probably--hot in Charlotte!! Should be lovely.
I would recommend staying on the NC side of the park, not Tennessee. The latter is more the gateway to Gatlinburg and Pigeon Forge--the shopping and crowded areas, I think.

Plans have changed...will be driving and not flying and travelling the 2nd week of July. Planning on staying in Townsend...how is the water flow of Little River in July?