Yikes!
Are you serious?! You live in New York City, are visiting Madrid, Spain, and are seeking an Irish Pub to eat?? Good God.
I avoid Irish Pubs like the black plague and have been inside only 2 since I started visiting Spain 13 years ago. They give me "the willies"! Blah! Make my skin crawl.
I know they're popular among Spaniards and other English people but they're so NON-Spanish! Why not just go to Ireland for vacation instead??
My English buddy tells me that Dubliners - one of the many Irish bars near Puerta del Sol - has a good English breakfast but I don't think these bars generally serve meals, just snack foods.
Stick to Spanish food. It'll improve your Spanish experience - and it's SO gooooood. :p :
Saludos, MadridMan