If you're looking for a meeting place or a good stop around ½ or halfway between Hollywood and Flagler Beach, you can try Palm Bay, FL, which is about 2 hours north of Hollywood, or almost 2 hours south of Flagler Beach.
About ¼ or a fourth of the way, you can stop at Jupiter, FL. This is almost an hour north of Hollywood.
About ⅓ or a third of the way, you can stop at Port Saint Lucie, FL. This is a little over 1 hour north of Hollywood.
About ⅔ or two thirds of the way, you can stop at Melbourne, FL. This is about 2½ hours north of Hollywood, or about 1½ hours south of Flagler Beach.
About ¾ or three fourths of the way, you can stop at Titusville, FL. This is almost 3 hours north of Hollywood, or about 1 hour south of Flagler Beach.
If you drive straight through without stopping at all, the total distance is 269 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, 54 minutes.