We have travelled this way many times, but not in the last 5 years or so. We have been on parts of 64 over on the west side quite recently. You will need to take I24 out of Chattanoogo up to Monteagle, then pick up 64. Just not much other way to get there. Monteagle will be about the steepest climb just don't get in a rush and you can make it OK. There is also 156 from Chattanooga over to US64, but not unless you are small and a lot of power, pull and steering both. Take your time and watch roadsigns for things to do. It is a very interesting drive with lots to see, just don't get in a hurry. Several good campgrounds on the way, Lawrensburg has Davie Crockett State Park, and I understand they have just finished a major campground upgrade.