Hi Florcastleman,
I am a guidance counselor in NY and the first thing you should do is go to your local enrollment office and get your children registered.  Check out the first link to understand what documents you will need to provide to enroll your children. Most of the information on the Department of Education website under how the admissions process works is for 9th grade students. You can contact the admissions office directly at: HS_Enrollment@schools.nyc.gov To find information about schools in your area, I have put three web resources (SchoolFinder: gives student: teacher ratio, demographic information and can help you find a school near your new address) (insideschools.org: provides reviews of local schools) (NYC Dept of Ed High School Directory: Hear from the school about its activities, classes, and mission) It is very important to research schools carefully -NYC high schools are very diverse in quality and safety. You can also read the progress report (how well the school is doing)  at 5th link below. If you don't like your children's placement, charter schools are another free option and can also be searched for on the three search sites I provided. To apply to a charter school, contact the school directly.

Best of luck and welcome!
Feel free to contact me with more questions.