Częstochowa, and the monastery of Jasna Góra is holy place for Polish and foreign Roman Catholics.
Katowice is the nearest airport, served by many LOT, Wizzair and Central Wings, it is about 1hrs taxi ride to Częstochowa town centre. Alternatively there are great (but slow) train links from all major Polish cities.
However many Polish Catholics take an annual pilgrimage to actually walk to Częstochowa in the summer months.
Częstochowa is rather small, and accommodations are easy to find. The monastery has a large guesthouse built to accommodate the immense amount of pilgrims who walk here annually from all over Poland. The only time of year you're likely to have a problem finding a place to stay is immediately before and after 15 August, the Feast of the Assumption - a Marian holiday which draws thousands to the monastery for special devotionals.
English speakers are easy to find near Jasna Góra - many nuns and priests on the grounds are multilingual. The town is another matter.
Some advice from a native local. Please be warned that in the area around Jasna Góra you can be approached by some shady individuals that will want to trick you into buying something. Don't be fooled -- your money will definitely not go towards costs of Jasna Góra renovation or charitable cause it will be probably spent on cheap booze.