For starters, the Hudson Valley was majority Dutch-speaking until about 1800. The language usage dropped off precipitously after that, but there were still old timers in the region speaking Dutch until nearly 1900.

I am unaware of any town in the Hudson Valley that was ever predominantly Irish, so I wouldn't really focus on Irish music. Dutch music from the 1600s and 1700s might be something you might want to explore. I'm not any expert on the music, so I can't give you guidance on that, but I do know that most towns in the Hudson Valley were "Dutch towns" or "English towns" for the first couple centuries. Poughkeepsie, Fishkill, and Peekskill were Dutch towns, for example, while West Point and Newburgh were English towns. New Paltz and Rhinebeck, meanwhile, were German-speaking towns. (In actual fact, all towns had some mixture of people, but were usually dominated by one or the other.)

Anyway, that's a long way of saying that it's probably better to focus on Dutch, English, early American, or possibly German music before 1800 to give an accurate portrayal of what was being listened to in the area back then.

More recently, in addition to the genres you mentioned, New York City was also home to the folk music scene in the 1940s and the "folk revival" in the early 1960s. The first wave produced the Weavers (including Pete Seeger) and Woody Guthrie. The latter produced Bob Dylan, Joan Baez, Phil Ochs, and the Even Dozen Jug Band, among others. They weren't all from New York, but they did all become famous through the New York City music scene. Most of them stayed in the city, except Dylan who famously moved upstate to Woodstock.

Speaking of which...there you go. The site of the original 1969 Woodstock festival is there in the Hudson Valley. That might make a good field trip destination.

If you're including New York City in your course, then, really, you can talk about virtually anything in the history of recorded American music. Jazz, ragtime, big band, rock and roll, you name it, it had a rich history there. Streisand, Sinatra, the Beastie Boys, the Velvet Underground, so many styles of music got there start there, you can make it anything you want.

NYC was one of 3 of the primary hubs for the development of jazz music in the first half+ of the 20th century; the other two being New Orleans, and Chicago. There is so much history to cover, but I'll just provide some key figures and locations that come to mind, due to the fact that you are looking into a broader variety of locations, and genres, and jazz is my only area of expertise when it comes to NYC.

Duke Ellington was the leader of the house band at the Cotton Club in Harlem from December 4, 1927, to June 30, 1931, his band stayed together for decades on, and these years are when he developed his quintessential orchestration techniques. He was a key figure in the Harlem Renaissance. NYC was also home to many dance clubs, such as the Savoy Ballroom in Harlem, and jazz clubs such as the Village Vanguard, which is still open to this day.

One of the most important developments when it comes to jazz came in the 1940s, and is very much tied to New York City. The style of Bebop came into fruition amongst many young virtuoso musicians. Minton's Playhouse, a club in Harlem, was a location where many young musicians such as Charlie Parker, Dizzy Gillespie, Thelonious Monk, and Bud Powell, would jam together and trade ideas which developed into a brand new style and philosophy regarding jazz music. It required extreme skill on one's instrument due to fast tempos, and the expectation of being able to improvise at a technically high level. This changed the course of jazz music from a genre primarily for dancing, to one that also served an artistic purpose meant for listening.

A variety of clubs opened on 52nd street in Manhattan, including but certainly not limited to the Onyx, the 3 Deuces, and Club Downbeat. Many of these clubs had signs that said "No Dancing" which gives credence to the change in philosophy amongst musicians, in that the music was the focal point, and that it should be listened to. "Hipster" culture developed during this time, which unlike "hipsters" today, was a subculture of individuals who were attempting to mimick the intellectual but also laid back mindset of jazz musicians. In fact, many wore the same kinds of berets and horn rimmed glasses that Dizzy Gillespie wore, and likewise adopted a similar fashion sense as the musicians.

Now, there are plenty of New York centric jazz musicians that you can read about throughout the '50s and '60s, and great developments in the music. But the important thing about Bebop is the scope of its influence. Charlie Parker and his other contemporaries were playing in a way that no one had heard before, and while he was from Kansas City, these developments happened partly due to the clashing of young minds in NYC. Their music influenced jazz musicians all over the United States, and from a musical standpoint, they codified a brand new language and "vocabulary" for improvising that was completely groundbreaking, and still studied by musicians today. The language they developed is often seen as the foundation for any musician trying to learn the music. If you want to talk about jazz at all, I think the Bebop movement is the place to start, as it's arguably the most revolutionary of movements that can be attributed specifically to New York City, in jazz of course.