If you're looking for a meeting place or a good stop around ½ or halfway between Santa Fe, NM and Los Angeles, you can try Williams Junction, AZ, which is about 6 hours west of Santa Fe, NM, or about 6½ hours east of Los Angeles.
Other possible places to stop near the midpoint include Chalender, Sereno Spring, Meath, Pinaveta, Crookton, and Audley.
About ¼ or a fourth of the way, you can stop at Gallup, NM. This is almost 3 hours west of Santa Fe, NM.
About ⅓ or a third of the way, you can stop at Winslow, AZ. This is about 4½ hours west of Santa Fe, NM.
About ⅔ or two thirds of the way, you can stop at Haviland, AZ. This is about 8 hours west of Santa Fe, NM, or about 4½ hours east of Los Angeles.
About ¾ or three fourths of the way, you can stop at Java, CA. This is about 9 hours west of Santa Fe, NM, or about 3½ hours east of Los Angeles.
If you drive straight through without stopping at all, the total distance is 848 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 12 hours, 24 minutes.