If you're looking for a meeting place or a good stop around ½ or halfway between Morrison and Carterville, you can try Chatham, IL, which is about 3 hours south of Morrison, or about 3 hours north of Carterville.
About ¼ or a fourth of the way, you can stop at Peoria, IL. This is a little over 1 hour south of Morrison.
About ⅓ or a third of the way, you can stop at Pekin, IL. This is almost 2 hours south of Morrison.
About ⅔ or two thirds of the way, you can stop at Edwardsville, IL. This is almost 4 hours south of Morrison, or about 2 hours northwest of Carterville.
About ¾ or three fourths of the way, you can stop at Germantown, IL. This is a little over 4 hours south of Morrison, or about 1½ hours northwest of Carterville.
If you drive straight through without stopping at all, the total distance is 355 miles. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 5 hours, 44 minutes.