Medjugorje is a pilgrimage town and the nightlife reflects that -- there are bars, but the village is quiet by eleven and properly asleep by midnight. Most pilgrims gather in the cafes around St. James' after the evening prayer service, drinking coffee and the local cherry brandy.
The square in front of the church has the largest cluster of cafes; almost all serve the standard Bosnian range of espresso, macchiato, and Turkish coffee, plus rakija and the local wines. Caffe Bar Galija, just off the square, is a long-running spot popular with both locals and pilgrims and stays open later than most. The bar at the Hotel Sunce, slightly out of the centre, has a quieter atmosphere if you want a glass of wine without the crowd.
A note: bars in Medjugorje will sell alcohol to anyone -- enforcement of age limits is essentially non-existent. If you are travelling with teenagers, this is worth knowing.