I did lots of teacher interviews before my kids came along, as department chair. And in the NY-NJ area, I would absolutely go with a suit-- and pantyhose if it's a skirt suit.
If you're really opposed to a suit, then get a black cardigan-- a good, kind of structured one, and wear it with a fairly conservative dress.
Other things to consider: try hard to be yourself, but your best self. Don't be afraid to make a small joke at your own expense or to ask a question if there's a term you're unfamiliar with. Remember, it's not the right answers they want so much as the right person. The best interviews are the ones where the conversation flows, kind of like a cocktail party minus the wine and cocktail franks.
Also, be very careful to remember: they don't care if it's your "dream job." (As an aside, I really hate that term!!!! I LOVE my job. But it's work, and there are days when it's incredibly hard work. ) Anyway, back to the point, they're not looking to be the good wish fairy; they don't care about your dream job. They're looking for their dream candidate. It's a fine distinction, but an important one.
Do your homework. Know about the school, the kids, the neighborhood. Know about Common Core and other important buzzwords. But I personally would suggest keeping them to a minimum unless they really fit in. I would much prefer a candidate who can say what she means in English than in edu-babble.
The best of luck to you. Let us know how it goes.