The correct pronoun choice depends on whether it is filling a Subject or an Object slot in the sentence syntax.
Subject pronouns are I, we, he, she, it, they, you, who. Subject pronouns follow to be verbs like, be, was, were, will am. is, are. Examples of Subject pronouns are: It is I. That will be they.
Object pronouns are me, us, him, her, it, them, you, whom. Object pronouns fill slots for the object(s) of a clause and the object of a preposition. Examples of Object pronouns are: He was calling (whom) me. That belongs to (whom) them.
In your clause, "The principal looked at we/us boys, ...," the pronoun fills the Indirect Object slot and therefore requires the Object pronoun. The Object pronoun of the Subject/Object pronoun pair we/us is us. The Object pronoun us answers "at whom?": The principal looked at whom? He looked at us.
"The principal looked at us boys, ...,"
You would say or write, "The principal looked at us boys..." The easiest way to determine which pronoun to use is to remove the noun(direct object) and read it again. "The principal looked at us" makes more sense than "The principal looked at we."
The principal looked at us boys, and I could see that she was wondering why we were behaving so crazily.
In this sentence, us is the object of the preposition at.
Hope this helps!
The principal looked at us boys,and I could see that she was wondering why we were behaving so crazily.
The pronoun after the preposition at must be an object.