If you're looking for a meeting place or a good stop around ½ or halfway between Fort Lauderdale and Miami, you can try North Miami Beach, FL, which is about 18 minutes south of Fort Lauderdale, or about 18 minutes north of Miami.
About ¼ or a fourth of the way, you can stop at Hollywood, FL. This is about 11 minutes south of Fort Lauderdale.
About ⅔ or two thirds of the way, you can stop at North Miami, FL. This is about half an hour south of Fort Lauderdale, or about 13 minutes north of Miami.
About ¾ or three fourths of the way, you can stop at West Little River, FL. This is about half an hour south of Fort Lauderdale, or about 8 minutes northwest of Miami.
If you drive straight through without stopping at all, the total distance is 28 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 37 minutes.