Whatever you do, avoid I=-24 thru Chattanooga. We just went to Smokys from north Alabama last Saturday 7/25 and returned 8/1. We found I-24 thru Chattanooga to be an insurmountable obstacle going and coming.
Going to the Smokys EB on 7/25 we came upon a dead stop that extended 10 miles into Chattanooga according to MapQuest. We got off on I-59 and took a 40 mile detour to the south.
Coming back WB on 8/1 we also found dead stops on I-24 on both sides of the I-75 exchange. Again we bailed out and took a detour south thru Georgia.
No one seems to know what the problem is, other than I-24 goes right thru the middle of town - no bypass.
Whatever you do, cut over to the east in time to avoid Chattanooga at all costs. I have officially written off that route.
You will eventually hit I-40 that would go to Knoxville that would be my choice this summer. Give us more details on where exactly you are going and we can give better guidance. For example, you do not want maneuver an RV from Pigeon Forge to Gatlinburg to get to the mountains.
2013 Tundra, 5.7FF, TRD, 4WD, tow pkg
2014 Forest River Cherokee 264
Prodigy II / Equalizer 10K
103 nights & 12,700 miles since April '13