Knoxville is a city in Tennessee.
Hitchhiking in Knoxville appears to be illegal per city ordinance 16-449. General solicitation restrictions.
It shall be unlawful for any person to solicit money or other things of value, or to solicit the sale of goods or services:
3) From any operator or occupant of a motor vehicle or from any person entering or exiting a motor vehicle.
Whether or not a "ride" counts could be questionable but it is technically something of value and the police seem intent on seeing it as such.
Outside of Knoxville on the westside on interstate 40 there is a cluster of truckstops (Flying J's, T.A. and a Petro) before you get out of town heading west theres a T.A. and a small Pilot sorry i dont know the exit but its the last one going west with a truck stop before you get to the big Flying J's and this T.A. Pilot exit would be your best bet to get to the flying j's, On the east side at exit 398 on interstate 40 theres a small pilot but i would suggest the onramp exit 407 which is just outside knox has some stuff gas stations and what not but also alot of cops cause kinda of a tourist area but if you get to like 415 i think theres a pilot and this is prolly your best bet for asheville and further points east but the onramp might be best here but you can try the pilot.
Going North on I-75: Check out this spot right here. Take bus number 20 from the city center (fare is $1,50) and get off at Tillery Drive. Walk 10 minutes and you're right there. The place offers gas stations, restaurants and a Starbucks, so the traffic is quite heavy.
Going East on I-40:
From downtown transit center, take bus #31-(Magnolia) to intersection of Asheville Hwy & S Chilhowee Dr. (last stop before bus turns back to downtown.) Last one leaves downtown at 23:15. From there, walk east about a quarter mile to on-ramp for hitching. Not much traffic but it will get you on your way, just be patient. If here at night, walk about another quarter mile east past I-40 for some discreet camping along river there that runs under Asheville Hwy.