If you're looking for a meeting place or a good stop around ½ or halfway between Wichita and Albuquerque, you can try Stevens, TX, which is about 4½ hours west of Wichita, or about 5 hours east of Albuquerque.
Other possible places to stop near the midpoint include Texhoma, Stratford, Brickel, Lautz, Chamberlin, Hitt, Wilco, and Rehm.
About ¼ or a fourth of the way, you can stop at Ford, KS. This is about 2 hours west of Wichita.
About ⅓ or a third of the way, you can stop at Liberal, KS. This is about 3 hours west of Wichita.
About ⅔ or two thirds of the way, you can stop at Tucumcari, NM. This is about 6½ hours southwest of Wichita, or about 3 hours east of Albuquerque.
About ¾ or three fourths of the way, you can stop at Palomas, NM. This is about 7 hours southwest of Wichita, or about 2½ hours east of Albuquerque.
If you drive straight through without stopping at all, the total distance is 595 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 9 hours, 38 minutes.