If you're looking for a meeting place or a good stop around ½ or halfway between Indianapolis and South Bend, you can try Peru, IN, which is a little over 1 hour north of Indianapolis, or a little over 1 hour south of South Bend.
Other possible places to stop near the midpoint include Cassville, Bennetts Switch, and Miami.
About ¼ or a fourth of the way, you can stop at Westfield, IN. This is about half an hour north of Indianapolis.
About ⅓ or a third of the way, you can stop at Goldsmith, IN. This is almost an hour north of Indianapolis.
About ⅔ or two thirds of the way, you can stop at Green Oak, IN. This is about 1½ hours north of Indianapolis, or almost an hour south of South Bend.
About ¾ or three fourths of the way, you can stop at Richland Center, IN. This is about 2 hours north of Indianapolis, or almost an hour south of South Bend.
If you drive straight through without stopping at all, the total distance is 150 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 2 hours, 34 minutes.