"What nationality was St. Patrick?" demands a guy at the door of the Public House, who isn't a bouncer, but still wants to enforce certain standards. Because even though there are other fine Irish bars, Price's Public House is the true center of Irish American nightlife in Cleveland. In the Irish neighborhood of West Park, a crowd of firefighters and union softball team members and other regular Joes and Colleens come together to drink $3 Guinness pints and listen to bands with names like the Portersharks and the New Barleycorn. No Yeats quotes on the walls here, no Celtic designs on the ceilings, but there is a sign in English and Celtic pointing the way to The Old Bog Road and a plaque commemorating every Notre Dame football victory in its 1977 national championship season. And instead of that "May the road rise to meet you" Irish blessing, a sign at the Public House offers a more practical bit of spiritual luck: "May you be in heaven half an hour before the Devil knows you're dead."252-6058.