If you're looking for a meeting place or a good stop around ½ or halfway between White Plains and Newark, you can try Paramus, NJ, which is about half an hour west of White Plains, or about half an hour north of Newark.
Another possible place to stop near the midpoint is Hillsdale.
About ¼ or a fourth of the way, you can stop at Grand View-on-Hudson, NY. This is about 12 minutes west of White Plains.
About ⅓ or a third of the way, you can stop at Spring Valley, NY. This is about 19 minutes west of White Plains.
About ⅔ or two thirds of the way, you can stop at Hackensack, NJ. This is about half an hour southwest of White Plains, or about half an hour northeast of Newark.
About ¾ or three fourths of the way, you can stop at Clifton, NJ. This is almost an hour southwest of White Plains, or about 14 minutes north of Newark.
If you drive straight through without stopping at all, the total distance is 49 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 57 minutes.