If you're looking for a meeting place or a good stop around ½ or halfway between Pompano Beach and Palm Beach, FL, you can try Boynton Beach, FL, which is about half an hour north of Pompano Beach, or about half an hour south of Palm Beach, FL.
About ¼ or a fourth of the way, you can stop at Boca Raton, FL. This is about 9 minutes north of Pompano Beach.
About ⅔ or two thirds of the way, you can stop at Lake Worth, FL. This is about half an hour north of Pompano Beach, or about 14 minutes south of Palm Beach, FL.
If you drive straight through without stopping at all, the total distance is 38 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 44 minutes.