If you're looking for a meeting place or a good stop around ½ or halfway between Fort Lauderdale and North 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 North Palm Beach.
About ¼ or a fourth of the way, you can stop at Deerfield Beach, FL. This is about 15 minutes north of Fort Lauderdale.
About ⅓ or a third of the way, you can stop at Boca Raton, FL. This is about 19 minutes north of Fort Lauderdale.
About ⅔ or two thirds of the way, you can stop at Lake Worth, FL. This is about half an hour north of Fort Lauderdale, or about 19 minutes south of North Palm Beach.
About ¾ or three fourths of the way, you can stop at West Palm Beach, FL. This is almost an hour north of Fort Lauderdale, or about 13 minutes south of North Palm Beach.
If you drive straight through without stopping at all, the total distance is 53 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 58 minutes.