Centerville opened in 84, still going, about 60 miles northwest of Little Rock, just west of the town on 672.
Closer to town I-30 Dragway, also called Excel-A-Rating Drag Strip and Little Rock Drag Strip is long gone , Pulaski Tech college is on that site, I30 Speedway oval is across the freeway. West of LR towards Benton. Ran from 1959 to the 80's
Carlisle was less than 30 miles east of LR ,on a taxiway at the local airport. Started in 55, closed around 89.
Further Northeast (80 miles or so from LR) is Newport which has a current 1/8th mile at the airport and had a 1000ft strip right beside there in the 80's
80 miles southwest gets you Prescott which ran then and still does. It is east of Prescott where 24 and 53 meet.
That is all we even know about in the 80's