What of the following important Supreme Court cases established a precedent of legal racial segregation in public places and was closely associated with the phrase separate but equal?

The important Supreme Court case that established the precedent of legal racial segregation in public places is Plessy v. Ferguson (1896). This ruling upheld the constitutionality of racial segregation under the "separate but equal" doctrine, which allowed states to maintain separate facilities for African Americans and whites as long as they were deemed equal. This decision legitimized segregation and discrimination for decades until it was eventually overturned by Brown v. Board of Education in 1954.