Each of the three answers a different devotion. At Łagiewniki, St. Faustina Kowalska, a young sister who died in 1938, recorded the message of Divine Mercy that has since spread through the whole Church; pilgrims pray at her tomb beneath the image inscribed “Jesus, I trust in You,” and the Hour of Mercy is prayed there every day at 3 p.m. Jasna Góra is far older: a monastery of the Pauline Fathers that has kept the icon of Our Lady of Częstochowa for six centuries and is the principal shrine of the Polish nation, reached on foot by walking pilgrimages every August.
St. John Paul II ties the places together. Karol Wojtyła was born in Wadowice in 1920 and baptized in the church on its market square; his family home is now a museum. He was a priest and then archbishop in Kraków, and as Pope he canonized St. Faustina in 2000 and made Divine Mercy Sunday a feast of the whole Church. A sanctuary dedicated to him stands a short walk from the Divine Mercy basilica. Many pilgrimages also include Auschwitz, where St. Maximilian Kolbe gave his life for another prisoner in 1941.
Good to know before you go: Kraków is the natural base, and all of these places can be reached from it as day trips, so there is no need to change hotels. Five to seven days is enough for a first visit. Poland is a country where the faith is still lived in public; go to an ordinary parish Mass on Sunday as well as to the shrines.