Pittsburgh is not the most Irish city in the country these days.
The early city was more or less founded by Scotch-Irish, which is now largely forgotten other than some local linguistic quirks that few know the roots of (like the terms redd up, nebby, and the second-person plural yinz, which came from you ones). The big migration of course came with the Great Famine, and unlike some areas like NYC and Boston, there really were no substantive later migrations, meaning ethnic cohesion was pretty much lost by the mid 20th century. Most of the remaining working-class Irish enclaves were disproportionately affected by white flight, so even though there are still identifiable "Italian" and "Polish" neighborhoods in the city, there are none with notable Irish heritage any longer.
That said, a few years back, I was invited to
a private Irish club here - It was an interesting experience, considering it's a faceless frame building on the outside, but has a fully-stocked Irish bar inside the first floor. I'm 1/4th Irish by ancestry, so I guess technically I could qualify but...why bother?