If you're looking for a meeting place or a good stop around ½ or halfway between Newport, RI and Cape May, you can try New York, NY, which is almost 3 hours west of Newport, RI, or about 3 hours north of Cape May.
Another possible place to stop near the midpoint is Yonkers.
About ¼ or a fourth of the way, you can stop at New Haven, CT. This is about 1½ hours west of Newport, RI.
About ⅓ or a third of the way, you can stop at Bridgeport, CT. This is almost 2 hours west of Newport, RI.
About ⅔ or two thirds of the way, you can stop at Howell, NJ. This is almost 4 hours southwest of Newport, RI, or about 2 hours northeast of Cape May.
About ¾ or three fourths of the way, you can stop at Toms River, NJ. This is about 4 hours southwest of Newport, RI, or about 1½ hours northeast of Cape May.
If you drive straight through without stopping at all, the total distance is 335 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 5 hours, 35 minutes.