If you're looking for a meeting place or a good stop around ½ or halfway between Newport, RI and Rochester, you can try Schenectady, NY, which is a little over 3 hours northwest of Newport, RI, or about 3 hours east of Rochester.
Another possible place to stop near the midpoint is Rotterdam.
About ¼ or a fourth of the way, you can stop at Springfield, MA. This is about 1½ hours northwest of Newport, RI.
About ⅓ or a third of the way, you can stop at Pittsfield, MA. This is about 2 hours northwest of Newport, RI.
About ⅔ or two thirds of the way, you can stop at Utica, NY. This is about 4 hours northwest of Newport, RI, or a little over 2 hours east of Rochester.
About ¾ or three fourths of the way, you can stop at Syracuse, NY. This is about 5 hours northwest of Newport, RI, or about 1½ hours east of Rochester.
If you drive straight through without stopping at all, the total distance is 420 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 6 hours, 25 minutes.