Where I live in NJ, you get to choose from 2 high schools. Whichever you pick must take you. This is not the case everywhere but is part of an effort to move students from the bigger school, the original “default” for our town, to another smaller one with more capacity. You may also enroll in other publics on a space available basis for tuition, which is not nominal, (and no bussing). This is, ime, something done rarely and only by families in which someone has a job in that area and can facilitate transportation.
But if the OP is moving to the area, presumably they are trying to create a list of neighborhoods where they could look at housing that would put them in the school district they want. This is a pretty common practice when relocating. Whether that housing is affordable and available is another question, but it’s a good place to start.