Are charter schools better than traditional public schools?

I would like to do a research about public schools in the Bronx in order to know which are the best ones. Moreover, I would like to know the most common problem between teachers, students and parents in the Bronx public schools. If something bad happen with any student, I would like to know where parents can go to complain and get effective results. I’m curious about this information because I have a daughter who is two years old, and soon she will need a good primary school that must be public because I cannot afford a private one. Also, I’m very worry about how public schools work in the Bronx because my sister in low told me that her daughter who is in the second grade almost fall from the second floor because a boy from six grade pushed her down the stairs. My sister in low went to complain to the teacher, and the teacher made fun of her complain. She said that she was in the front, and she could not see what was happening in the back. This is something that I consider serious because something bad could happen to my niece and that teacher just laughed about it. My sister in low told me that she is not the only mother complaining about the bad operation of that school. She told me that a teacher was suspended. However, she told me that now the problem is worst because the principal and the teachers protect each other. My niece is in a traditional public school, and I would like to know if charter schools are better than the traditional public schools.