There are (or used to be, a few years ago) at least 4 "Irish" pubs in Rome with traditional music. The best of these, IMHO, were the Druid's Den and the Fiddler's Elbow, both near Santa Maria Maggiore church, not far from Termini. When I was living in Naples we travelled up every Thursday for the Druid's Den session. There were on average 10-12 musicians there every week, including two harpists, playing Irish music, of which I was the only Irish person. The Rome musicians used to meet in other places in Rome, and played not only Irish but also Neapolitan and Italian folk music, but living in Naples I wasn't able to get to their other sessions. There were two restaurants on the other side of Termini that had Ethiopean or Eritrean music, which were patronised by Somalis, who in turn knew of other places with similar music.