Don't count on it! The public school systems in the NYC suburbs (including NJ) have been the same since the 1970's - 1980's. Before then, most suburban school districts were 90%+ white. Then between the 1980's - 2000's, a lot of white flight took place in some suburbs and those suburbs became heavily minority. From the early 2000's politicians have tried various methods to improve the schools and most of them failed. The result today is there is a HUGE education gap between those school districts in wealthy mostly white neighborhoods and schools in low income mostly minority neighborhoods. Yes, this includes Hoboken.
The real shame of it is that Mark Zuckerberg, CEO of Facebook announced on Oprah that he was donating $1 million to fix Newark public schools a few years ago. Well, now that the money was spent, the public schools in Newark are just as bad as they were before Mark donated $1 million.
So to answer your question - if $1 million cannot fix the school system in Newark, what makes you think anything will change in nearby Hoboken? If home's are cheap in Hoboken, there is a reason for it.