If you're looking for a meeting place or a good stop around ½ or halfway between Newport, RI and Syracuse, you can try Albany, NY, which is about 3 hours northwest of Newport, RI, or about 2½ hours east of Syracuse.
Other possible places to stop near the midpoint include Van Deusenville, Alford, Pittsfield, Rayville, Arnolds Mill, Nassau, Valatie, East Chatham, Wemple, and Hannacroix.
About ¼ or a fourth of the way, you can stop at Belchertown, MA. This is about 1½ hours northwest of Newport, RI.
About ⅓ or a third of the way, you can stop at Springfield, MA. This is about 1½ hours northwest of Newport, RI.
About ⅔ or two thirds of the way, you can stop at Rotterdam, NY. This is about 3½ hours northwest of Newport, RI, or about 2 hours east of Syracuse.
About ¾ or three fourths of the way, you can stop at Berryville, NY. This is almost 4 hours northwest of Newport, RI, or about 1½ hours east of Syracuse.
If you drive straight through without stopping at all, the total distance is 338 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, 19 minutes.