I just returned from a visit with family in NC. I took Illinois 47 to get around Chicago (great scenery and you avoid the Chicago traffic hassle). Took it all the way south to Champaign, where I took I-74 east to Indiana 63 to Terre Haute. Then US-41 south to Nashville. It and 63 are all four lane. The only towns you have to drive through are Terre Haute and Evansville.
Gas in Henderson, Ky, just across the Ohio River was the cheapest, under $2 on my way down on November 20th and $2.14 on the way back on Dec. 5th. In Henderson, you can go on the Pennyrile Parkway to Hopkinsville, Ky. It used to be a toll road, but, believe it or not, it no longer is. It is slated to become part of the I-69 corridor. (That jus' doesn't happen around Chicago.)
Then I-40 to Raleigh, and US-70, all four lane to Goldsboro, NC.
A word of caution about gas stations off I-40 in the Chapel Hill, Durham, and Raleigh area. If you don't see signs by the interstate, you might be in for a long ride to get to one. I got off at one Chapel Hill exit and gave up after a couple miles. Then I got off at an exit for Jordan Lake and went south for five miles before getting to a station.
Also, if you see a Smithfield's Chicken and BBQ place along the way, stop and have some of that great Carolina pulled pork, vinegar-based bbq, hush puppies, cole slaw, and sweet tea. Just the thing to slake your hunger after a long day out on the road.