The correct verb choice for "One of my friends is going to (part B)" hinges on subject-verb agreement. The subject, "one," is singular, requiring a singular verb. Thus, "is" is the appropriate verb, resulting in: "One of my friends is going to (part B)."
"Is" correctly agrees with the singular subject "one."
"Are" and "were" are plural and do not agree.
"Was" is singular but incorrect due to its past tense, which doesn't fit the sentence's present context.