If you're looking for a meeting place or a good stop around ½ or halfway between Central Point and Fallon, you can try Old Station, CA, which is almost 3 hours southeast of Central Point, or about 3½ hours northwest of Fallon.
Other possible places to stop near the midpoint include Halls Flat, Norvell, and Westwood Junction.
About ¼ or a fourth of the way, you can stop at Hotlum, CA. This is about 1½ hours southeast of Central Point.
About ⅓ or a third of the way, you can stop at Esperanza, CA. This is about 2 hours southeast of Central Point.
About ⅔ or two thirds of the way, you can stop at Janesville, CA. This is about 4 hours southeast of Central Point, or a little over 2 hours northwest of Fallon.
About ¾ or three fourths of the way, you can stop at Scotts, CA. This is about 4½ hours southeast of Central Point, or about 1½ hours west of Fallon.
If you drive straight through without stopping at all, the total distance is 369 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 6 hours, 9 minutes.