Medjugorje runs on the Catholic calendar. The two great peaks are Easter -- floating between late March and late April -- and the anniversary of the first apparitions on 25 June, which expands into a week-long youth festival in early August. The village is full to bursting during both, and accommodation needs booking months in advance.
For a quieter visit, May, September, and October are ideal. The weather is warm but not hot, the crowds thinner, and the wine harvest in October brings a good mood to the village. Summer (July, August) is hot -- temperatures can hit 35 C -- and the climbs to Apparition Hill and Cross Mountain are best done early in the morning. Winter is cool, mostly dry, and very quiet; most pilgrim guesthouses scale back, but the church services continue.