There are too many places to hit up there - but every trip to NY needs to be met with three things. A vendor dog, a slice of good NY style pizza and a delicious cheese cake. After that, all else is up for grabs.
I really liked going to Ellis Island, and it could be a really great thing for you to have in your repetoire, as a school teacher. I also am a BIG fan of the American Natural History Museum, which is conveniently located next to Central Park. There's a
really cool castle inside of Central Park that I think everyone should see in person... There's so much. It's really hard to go wrong in NYC.
Oooh, if modern art's your thing, I also had a really good time at MOCA on my last visit. When I went there, I just had to wait outside in the rain for a while, since it had just re-opened and people were clamoring to get a peek. Might not be as busy these days.
If/When I think of more, I'll post.