If you're looking for a meeting place or a good stop around ½ or halfway between Newport, RI and Gettysburg, you can try Elizabeth, NJ, which is about 3½ hours west of Newport, RI, or about 3 hours east of Gettysburg.
Another possible place to stop near the midpoint is Edison.
About ¼ or a fourth of the way, you can stop at Bridgeport, CT. This is almost 2 hours west of Newport, RI.
About ⅓ or a third of the way, you can stop at Stamford, CT. This is a little over 2 hours west of Newport, RI.
About ⅔ or two thirds of the way, you can stop at Allentown, PA. This is a little over 4 hours west of Newport, RI, or a little over 2 hours northeast of Gettysburg.
About ¾ or three fourths of the way, you can stop at Pottsville, PA. This is about 5 hours west of Newport, RI, or about 1½ hours northeast of Gettysburg.
If you drive straight through without stopping at all, the total distance is 390 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.