First filter.
You got proposals? I shouldn't be surprised. Who's teaching you?
I have - I've been here almost two years and museums are a good way to get a quick snapshot of history so I spent some time doing that when I first arrived. The Intrepid Sea, Air & Space Museum might be of interest, the Natural History museum as well. The Metropolitan Museum of Art and the Museum of Modern Art are both art museums, so you may not find them as interesting in topic, but again useful for cultural reference.
It's a bit of a drive, or train ride if you'd rather, but I found the Smithsonian's in DC to be really interesting as well. The American History one was better than the history book I read. But if you've got time and you'd like to know about where you're at? They're worth an afternoon spent I think -- especially if you've good company.