Staten Island University Hospital system is owned by Northwell (then North Shore - Long Island Jewish), which announced several years ago that all new hires across their system had to have the BSN. How that has played out cannot say since there is only one BSN undergrad on Staten Island (Wagner College), the others are ADN then RN-BSN (The College of Staten Island), or just ADN (St. Paul's).
Am not qualified to give accurate advice on current working conditions and so forth for S.I. hospitals. You can Google and or search the archives of this forum for information. Also check out our local town newspaper (Staten Island Advance/SILive.com)
As for schools, what are you looking for, public or private?
By and large the better public pre-K to grade schools are Mid-Island and or on the South Shore (roughly area just north of Staten Island Expressway, and or south of it ), but this varies by neighborhood. High schools are another thing all together. Many parents will put their kids in private (religious or otherwise) high school after doing public grade school.
How they scored: Top 1 Staten Island schools in reading, math | SILive.com
Staten Island Schools - Staten Island New York School Ratings - Public and Private
Staten Island New York School Ratings and Reviews | Zillow
Yes, nurses on Staten Island travel to Brooklyn, Manhattan, and even New Jersey. Know of a few that go from SI to Lutheran Medical Center in Brooklyn for instance.
Traffic on Staten Island is a hot mess; especially the SIE (Staten Island Expressway). Your commute off and back to SI will largely depend upon how you choose to go and where you are going.
Don't overlook lower Manhattan (New York-Presbyterian/Lower Manhattan Hospital (formerly Beekman Downtown Hospital), as it is literally a short walk from South Ferry. NewYork-Presbyterian Careers | Job Search | Registered Nurse - RN - Emergency Department - Per Diem