If you're looking for a meeting place or a good stop around ½ or halfway between Ramnicu Valcea and Tarnaveni, you can try Sibiu, Romania, which is about 1½ hours north of Ramnicu Valcea, or about 1½ hours south of Tarnaveni.
Another possible place to stop near the midpoint is Cisnadie.
About ¼ or a fourth of the way, you can stop at Caineni, Romania. This is almost an hour north of Ramnicu Valcea.
About ⅔ or two thirds of the way, you can stop at Seica Mare, Romania. This is about 2 hours north of Ramnicu Valcea, or almost an hour south of Tarnaveni.
About ¾ or three fourths of the way, you can stop at Copsa Mica, Romania. This is a little over 2 hours north of Ramnicu Valcea, or almost an hour south of Tarnaveni.
If you drive straight through without stopping at all, the total distance is 177 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 2 hours, 55 minutes.