While I've never sat in the boxes, the AA theatre if memory recalls has a very long mezzanine. I can't imagine the boxes are too good and would be quite off to the side. Although, more than most other Broadway houses - who knows..
I've sat in both the mezzanine and orchestra boxes at the AA Theater. Both have pretty bad views. The level of obstruction depends on the layout of the set, but you're pretty much guaranteed to miss at least a few moments. If you have to have a box, I would go with the mezzanine since it tends to provide slightly better views than the orchestra ones. I would try to get a non-box seat though. All of the seats in that theater have great leg room if that's part of the reason you were looking at the boxes. The rear mezz should have equal or lower prices, and would provide a much better view.