Located in Łagiewniki, within convenient 5mins walking distance of the Sanctuary of Divine Mercy, the ambitious ‘Have No Fear!’ John Paul II Centre (the official name of which refers to his famous words during his inauguration speech) is a large complex devoted to the legacy and spiritual teachings of every Pole’s favourite Pope, including many facilities for pilgrims. The primary highlights for visitors are the Sanctuary of St. John Paul II - a chapel with relics of the former pope, including a vial of his blood and the blood-stained cossack he was wearing during the 1981 assassination attempt on his life (open 07:30-18:00, in summer 07:30-19:00; sanktuariumjp2.pl; free (donation-based) guided tours in English available); the John Paul II Institute - where visitors will see a copy of the Shroud of Turin (open 08:00-16:00, closed Sat, Sun; free admission); the Archdiocesan Museum of St. John Paul II - which displays the personal belongings of the Pope and a rich collection of papal gifts received during his world travels (opening hours subject to change, check online at archimuzeum.pl; admission 10/6zł); and the observation tower - from which you'll see panoramic views of the surrounding area (open from April until mid-October only, 09:00-17:00; 4/2zł). There is also a cafe serving the Pope's beloved 'kremówka' cake (note that there's no other proper food available).
Getting to the John Paull II Centre is a bit complicated. A cab will cost you about 20-30zł, or take tram 8 or 22 to the end of the line at 'Borek Fałęcki' and walk about 10mins (you'll need to buy a 4.60zł single-journey tram ticket). There is also a 'Papal Bus Service' which runs direct from Bishop's Palace (ul. Franciszkańska 3) to the JPII Centre every hour on the hour from 09:00-18:00 (ticket 10zł).
Sanctuary of Divine Mercy
ul. Św. Siostry Faustyny 3 (Łagiewniki)