If you're looking for a meeting place or a good stop around ½ or halfway between Houston and Floresville, you can try Dubina, TX, which is about 1½ hours west of Houston, or almost 2 hours northeast of Floresville.
Other possible places to stop near the midpoint include High Hill, Schulenburg, Engle, and Praha.
About ¼ or a fourth of the way, you can stop at Brazos Country, TX. This is about half an hour west of Houston.
About ⅓ or a third of the way, you can stop at Bernardo, TX. This is almost an hour west of Houston.
About ⅔ or two thirds of the way, you can stop at Sandy Fork, TX. This is about 2 hours west of Houston, or about 1 hour northeast of Floresville.
About ¾ or three fourths of the way, you can stop at Belmont, TX. This is a little over 2 hours west of Houston, or almost an hour northeast of Floresville.
If you drive straight through without stopping at all, the total distance is 197 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 3 hours, 4 minutes.