As someone who has actually immigrated to America twice, this is a group of songs very dear to my heart and I keep hearing great ones all the time.
Although it's been done 1,000,000,000 times or more, "Spancil Hill," particularly when you know the story behind the song, still stands out as a great one. "Edward Connors" is another. The older, local version of "The Shamrock Shore" (later "Paddy's Green Shamrock Shore") sung around Inishowen is a fine song. The fact is, there are so, so many.
Among modern songs, I like "Slip Jigs and Reels" as well as any.
All the best,