If you live in NYC, you might be underwhelmed. I toured a couple years ago, and my main reaction was "This looks like a bigger version of my current apartment!" A huge percentage of the walk-up buildings in Manhattan are from the tenement era, so it's pretty likely that you or a friend already live in one.
I live in NYC with my wife and two kids in a 1 bedroom unit in a prewar building. I've never been to the Tenement Museum and it sounds like I don't need to.
That was the most interesting part to learn about for me, but they don't have the outhouses, and many of the tours are in units that were retrofitted with indoor plumbing and bathrooms later. Those units look essentially the same as they do now, except they have older furniture and kitchen fittings.
https://www.tenement.org
https://www.tenement.org/visit/tenement-apartment-tours/