If you're looking for a meeting place or a good stop around ½ or halfway between Palmdale and Mountain Top Junction, you can try Llano, CA, which is about half an hour east of Palmdale, or about half an hour northwest of Mountain Top Junction.
About ¼ or a fourth of the way, you can stop at Littlerock, CA. This is about 12 minutes southeast of Palmdale.
About ⅓ or a third of the way, you can stop at Pearblossom, CA. This is about 17 minutes southeast of Palmdale.
About ¾ or three fourths of the way, you can stop at Pinon Hills, CA. This is about half an hour east of Palmdale, or about 15 minutes northwest of Mountain Top Junction.
If you drive straight through without stopping at all, the total distance is 43 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 53 minutes.