Interstate 80
The best way to travel from Nashville Tennessee to Knoxville Tennessee is by Interstate 40.
Interstate - 5.
The fastest and shortest way would be to take Interstate 55 North, then Interstate 57 North.
On Interstate highway 90 East as the fastest driving route.
Travel to Annapolis, MD from the North is best completed via the following interstate route: 95 South to 895 South, to 97 South. 97 will end at route 50 East from which one can follow signs to the Visitor Center. From the South, the route is interstate 95 North to 495 N to route 50 East from which one can follow signs to the Visitor Center.
Qew west to hamilton.continue on qew.then merge onto the 405 to Lewiston Bridge .then to I-190 N .exit at Route 33 Arrive at Buffalo,NY
Take U.S. 26 EAST to I-25. Follow signs. You want I-25 NORTH to the MIDWEST.Take I-25 NORTH to Buffalo.
It's difficult to give a definitive answer. Buffalo to Memphis would be very different directions than Manhattan to Knoxville. In case it's the latter, take the Holland Tunnel to I-78 West to I-81 South to I-40 West. It's a little over 700 miles, should take around 11 hours of driving.
Interstate 40 runs from all the way from Barstow, CA to Nashville. That's the easiest and fastest. You get to I-40 from I-15.
Google Maps estimates the driving time as 8.5 hours via Birmingham and Montgomery on Interstate 22 which is 12 minutes faster although it is 20 miles longer then the shortest route.
Interstate 80 connects the two. If you drive across the George Washington Bridge, you won't have to make any turns.