Using coordinates:
Midpoint = ((38.6+32.8)/2, (-90.2-96.8)/2) = 35.7° N, 93.5° W.
This point falls near Mount Ida, Arkansas (Montgomery County), in the Ouachita National Forest—roughly 300 miles from each city via I-30/I-40.
Via I-30/I-40, the halfway driving distance (~310 mi each way) is around Little Rock, AR.