School availability info without address?

Parents — is there a research spot where I can gauge the likelihood of public school availability/placement based on different locations?

Planning a family relocation (girls will be 4 and 2 this August) — and having trouble narrowing our neighborhood search.

We are looking for a 30 minute subway commute to midtown, but very open to neighborhoods and willing to sacrifice space for location for our first apartment.

Availability of public 4k in a school (in a place with availability in paid 2s program) would majorly determine our priorities, but I can’t even make a myschools.nyc account without an address.

My nightmare scenario is we work our asses off to find/secure the ideal place for our work commutes only to find out after we’re locked in that the close-by school is full and the next-closest option totally fucks us logistically.

I am fully willing to do the research legwork but cannot figure out where to look. Is there such a place?

Thank you for your advice —