I stayed at the Armagh City Hostel in October of 2002. I generally prefer private hostels, but this one is so laid back it was just as good. The facilities are brand new and private rooms were available with tv, shower and wc for little more than some dorm accomodations.
Nice tv lounges, kitchen, laundry and view overlooks the football field. It's on one of the hills next to St. Patrick's Cathedral and a short walk to all the attractions. The manager, John, is great and you can come and go as you please with a key code.