If you're looking for a meeting place or a good stop around ½ or halfway between Las Vegas and Cedar City, you can try Mesquite, NV, which is a little over 1 hour northeast of Las Vegas, or a little over 1 hour southwest of Cedar City.
Another possible place to stop near the midpoint is Littlefield.
About ¼ or a fourth of the way, you can stop at Ute, NV. This is about half an hour northeast of Las Vegas.
About ⅔ or two thirds of the way, you can stop at Saint George, UT. This is about 1½ hours northeast of Las Vegas, or almost an hour southwest of Cedar City.
About ¾ or three fourths of the way, you can stop at Washington, UT. This is about 2 hours northeast of Las Vegas, or about half an hour southwest of Cedar City.
If you drive straight through without stopping at all, the total distance is 170 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 2 hours, 29 minutes.