I spent Labor Day walking around the Lower East Side ("LES"). It was about 15 miles in total and I think I passed the halfway point of the project (254 miles) along the way.
The LES was traditionally a working-class / immigrant neighborhood. [Sidebar: That's not very descriptive though, is it? I mean, with only a few exceptions, most areas of Manhattan were immigrant neighborhoods at one time or another, and probably working-class too. In 1910, when Manhattan's population peaked at 2.3 million (it's about 1.6 million today), 41% of New Yorkers were foreign born. By default that would have given a lot of neighborhoods at least some immigrant character. Sidebar over.]
The LES in particular though was known for its crowded, squalid tenements. In 1884 there were 334,000 people in a single square mile of the LES, making it the most densely populated place in the world (compare that with about 50,000 per square mile in Manhattan today). The old tenement buildings still remain, but I'm pretty sure that indoor plumbing and other modern amenities have been added to most of the apartments. For a view of what it used to be like, you can visit the Tenement Museum at Orchard and Delancey (I've never been, but I hear it's cool).
Chinatown (to the west) has grown and now extends into the western streets of the LES. You see a lot of Chinese restaurants and businesses in the area and the fish markets give you an idea of what the neighborhood might have smelled like in the tenement era.
The area is also home to the three bridges connecting Manhattan to Brooklyn. From north to south, they are the Williamsburg Bridge (1,600 ft. span / opened 1903), Manhattan Bridge (1,480 ft span, opened 1909), and the Brooklyn Bridge (1,596 ft. span / opened 1883).