I had a hard time finding good information about public schools in Yonkers. This is the website for the school district: https://www.yonkerspublicschools.org
If you need to register your children for school you will have to book a time to bring your documents in person. The phone number is: +1 914-376-8000. I was told I would have to wait at least two weeks for an appointment, so call them early.
The school district is located in the same building as the public library in downtown Yonkers, across from the train station. The address is
Curbside parking is next to impossible in that part of Yonkers, so I recommend the parking garage at 99 Hudson St, Yonkers, NY 10701