If you're looking for a meeting place or a good stop around ½ or halfway between Newport News and Norfolk, you can try Woodbine, VA, which is about 11 minutes south of Newport News, or about 13 minutes west of Norfolk.
Another possible place to stop near the midpoint is Armistead Forest.
About ¼ or a fourth of the way, you can stop at River Shore, VA. This is about 7 minutes south of Newport News.
About ⅓ or a third of the way, you can stop at Dunedin, VA. This is about 9 minutes south of Newport News.
About ⅔ or two thirds of the way, you can stop at Pinehurst, VA. This is about 15 minutes south of Newport News, or about 9 minutes west of Norfolk.
About ¾ or three fourths of the way, you can stop at Portsmouth, VA. This is about 17 minutes southeast of Newport News, or about 7 minutes southwest of Norfolk.
If you drive straight through without stopping at all, the total distance is 21 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 24 minutes.