Medjugorje is tiny. The village core -- St. James' Church, the cafes, the pension strip -- is fifteen minutes end to end on foot, and most pilgrims do everything on foot. Apparition Hill (Podbrdo) is about 2.5 km from the church, an easy walk along the road; Cross Mountain (Krizevac) is closer, perhaps 1.5 km, and the climb starts at the edge of the village.
For day trips and onward travel, taxis are easy to find at the church square and reasonably priced. A car can be rented through one of the hotels or a local agency (try Globtour); roads in Herzegovina drive on the right, signs are in Croatian, and traffic is light. The closest big-name car rentals are at Mostar airport.