If you're looking for a meeting place or a good stop around ½ or halfway between Fort Lauderdale and West Palm Beach, you can try Delray Beach, FL, which is about half an hour north of Fort Lauderdale, or about half an hour south of West Palm Beach.
About ⅓ or a third of the way, you can stop at Deerfield Beach, FL. This is about 16 minutes north of Fort Lauderdale.
About ⅔ or two thirds of the way, you can stop at Boynton Beach, FL. This is about half an hour north of Fort Lauderdale, or about 18 minutes south of West Palm Beach.
About ¾ or three fourths of the way, you can stop at Lake Worth, FL. This is almost an hour north of Fort Lauderdale, or about 11 minutes south of West Palm Beach.
If you drive straight through without stopping at all, the total distance is 46 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 51 minutes.