Assuming you're taking I-44, the halfway point is near Plano, Missouri but locations in the west part of Springfield are close enough.
Morton, IL
Van Horn, TX
Kansas
Around/between Charleston and Arcola IL, depending on what route you take.
According to MeetWays, halfway between Cheyenne, Wyoming and Wichita, Kansas would be a point near Brewster, Kansas on I70.
The halfway point between Peoria and Topsail Island is Point Pleasant, WV, on US-35 just on the West Virginia side of the Ohio state line. (Route highlights: I-74 to I-70 to US-35 to I-77 to I-74 to I-40)
Kansas City, Missouri.
Salina Kansas
The halfway point between Melbourne and London is Akyab, Myanmar.
Westfall, Kansas.
Rishel, Kansas.
Terre Haute, IN