If you're looking for a meeting place or a good stop around ½ or halfway between Houston and Ozona, you can try San Antonio, TX, which is almost 3 hours west of Houston, or about 3 hours southeast of Ozona.
About ¼ or a fourth of the way, you can stop at New Bielau, TX. This is a little over 1 hour west of Houston.
About ⅓ or a third of the way, you can stop at Brown Hill, TX. This is about 1½ hours west of Houston.
About ⅔ or two thirds of the way, you can stop at Kerrville, TX. This is about 3½ hours west of Houston, or a little over 2 hours east of Ozona.
About ¾ or three fourths of the way, you can stop at Noxville, TX. This is about 4 hours west of Houston, or about 1½ hours east of Ozona.
If you drive straight through without stopping at all, the total distance is 398 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, 42 minutes.