If you're looking for a meeting place or a good stop around ½ or halfway between Philadelphia and Doylestown, you can try Cold Point, PA, which is about half an hour northwest of Philadelphia, or about half an hour southwest of Doylestown.
Another possible place to stop near the midpoint is East Oreland.
About ¼ or a fourth of the way, you can stop at Andorra, PA. This is about 14 minutes northwest of Philadelphia.
About ⅓ or a third of the way, you can stop at Ivy Rock, PA. This is about half an hour northwest of Philadelphia.
About ⅔ or two thirds of the way, you can stop at Spring House, PA. This is about half an hour north of Philadelphia, or about half an hour southwest of Doylestown.
About ¾ or three fourths of the way, you can stop at Montgomeryville, PA. This is almost an hour north of Philadelphia, or about 14 minutes southwest of Doylestown.
If you drive straight through without stopping at all, the total distance is 42 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 59 minutes.