Manhattan: SAB, JKO, BAE, FAB, Alvin Ailey, BH, Ellison, Ballet tech. There are a few more but this should be a good start. BH may not be quite as good as the others but they may be less expensive and they are still offer good solid training. (Stay away from Joffrey it’s crowded and not that good.)
Brooklyn: Mark Morris, Brooklyn Ballet.
Keep in mind that there are scholarships if your child is born gifted. Ballet Tech is free as it is a public school. It starts at 4th grade so maybe for next year if your daughter is in the third grade now. Depending on your ethnicity you may want to look into DTH as they have outreach programs. Mark Morris has a beautiful studio but not quite at the level of some of the schools in Manhattan. Gelsey Kirkland also has a school in Brooklyn but it is both small and expensive and I hesitate to recommend it for those reasons.
Edit: I see from another question that your daughter takes Jazz classes. If she is serious she should be taking ballet classes and drop jazz for now until she is older and builds some solid ballet technique. Even if ballet isn’t her goal. Ballet is where she will build strong dance technique which is useful for other dance genres. Taking both ballet and jazz at the same time creates muscle confusion. Especially for someone so young just starting out. Jazz can be added once her technique in ballet is well established. Then it Isn't a problem doing both.
If you decide to stay recreational but want a better recreational school, any school that allows jazz before taking ballet is not going to be a better school. Make sure the studio floors are sprung or floating to help keep your child from injury and check where the teachers have danced professionally and where the teachers have trained.
Obviously stay away from any competition school as they offer poor teaching in regards to proper form and often are more expensive than far better professional schools. Not to mention competition training puts your child at greater risk for injury as those schools push dance tricks over proper form.
My daughter is a professional concert contemporary dancer & choreographer. Ballet academy trained. Dance grad of LaGuardia Arts high school (the FAME school.) Graham & Horton modern trained. Juilliard SI. BFA in dance from NYU Tisch. Currently choreographing and performing in a world renown concert contemporary company.
I worked for NYCB (New York City Ballet.)