If you are looking for cooler weather driving distance from Texas, we love Banner Elk, NC. It is not close to memphis but you could drive through memphis on the way there and back. The Smoky Mountains are great and cooler than Memphis and Texas, but the altitude is not high enough to keep it cool in the summer. The high in Gatlinburg on July 4th ,2011 was 93 and low was 69.
I own a 4th of July week at Blue Ridge Village in Banner Elk, NC and the summer weather is WONDERFUL. The altitude of 4000 feet is much higher than Gatlinburg and so it is much cooler here. The high for 4th of July 2011 was 82 and the low was 59. Ofen during 4th of July week the high is mid 70's with lows in the lower 50's. We love the area and ESPECIALLY getting away from the heat in the summer. Not sure if you want cooler weather or Memphis area more, but if it is cool weather you are looking for I highly recommend the Banner Elk/ Blowing Rock area in the High Country of the Blue Ridge Mountains.