If you're looking for a meeting place or a good stop around ½ or halfway between Peru and Lansing, IL, you can try Tyner, IN, which is about 1 hour north of Peru, or a little over 1 hour east of Lansing, IL.
Other possible places to stop near the midpoint include Koontz Lake, and Grovertown.
About ¼ or a fourth of the way, you can stop at Big Hill, IN. This is about half an hour north of Peru.
About ⅓ or a third of the way, you can stop at Plymouth, IN. This is almost an hour north of Peru.
About ⅔ or two thirds of the way, you can stop at Valparaiso, IN. This is about 1½ hours northwest of Peru, or almost an hour east of Lansing, IL.
About ¾ or three fourths of the way, you can stop at Chesterton, IN. This is almost 2 hours northwest of Peru, or about half an hour east of Lansing, IL.
If you drive straight through without stopping at all, the total distance is 124 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, 15 minutes.