About ¼ or a fourth of the way, you can stop at Tullamore, Ireland. This is about half an hour northeast of Birr.
About ¾ or three fourths of the way, you can stop at Kilcock, Ireland. This is about 1½ hours northeast of Birr, or about half an hour west of Dublin.
If you drive straight through without stopping at all, the total distance is 142 km. 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 1 hour, 50 minutes.