I think it's probably best to be at your intended viewing location at least a couple hours before the eclipse. I would definitely avoid big metro areas like St. Louis or Nashville if possible. Major interstates near the path of totality will probably be OK a few hours before the eclipse. Interstates that connect directly to large cities like I-55 and I-70 in Illinois, I-65 in IN/KY, and I-75 in KY may be pretty busy early in the day if people are driving south for the day.
I'm considering going to Sparta, TN because it isn't near any north-south interstates and it's also not really that close to I-40, so traffic shouldn't be bad a few hours before the eclipse.