If you're looking for a meeting place or a good stop around ½ or halfway between Newport, RI and Poughkeepsie, you can try New Britain, CT, which is about 1½ hours west of Newport, RI, or almost 2 hours east of Poughkeepsie.
Other possible places to stop near the midpoint include Newington, and Meriden.
About ¼ or a fourth of the way, you can stop at Norwich, CT. This is almost an hour west of Newport, RI.
About ⅓ or a third of the way, you can stop at Colchester, CT. This is about 1 hour west of Newport, RI.
About ⅔ or two thirds of the way, you can stop at Southbury, CT. This is a little over 2 hours west of Newport, RI, or about 1 hour east of Poughkeepsie.
About ¾ or three fourths of the way, you can stop at Danbury, CT. This is about 2½ hours west of Newport, RI, or almost an hour southeast of Poughkeepsie.
If you drive straight through without stopping at all, the total distance is 183 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 3 hours, 17 minutes.