Ulster, Munster, Leinster and Connacht, were all kingdoms. There were actually five of them:
Uladh - Ulster
Cruachain - Connaught
Midhe & Breda - Meath
Laigin - Leinster
Mumhan - Munster

Songs about places is not specifically stronger in Ireland than elsewhere. Looking at the link provided as an indication of that, I dare say that you could come up with a similar tourists guide of a song book about anywhere in the British Isles.