A question tag is a short question at the end of a statement. Here's why "did they?" is correct:
Identify the Auxiliary Verb: The main verb in the sentence is "did not go." The auxiliary verb used for negation and past tense is "did."
Opposite Polarity: The main statement "They did not go to Vienna last week" is negative. Therefore, the question tag must be positive.
Match the Subject: The subject of the statement is "They," so the pronoun in the question tag must also be "they."
Putting it together:
Therefore, the complete sentence is: "They did not go to Vienna last week, did they?"
