Taiwan Diplomatic Review Act This bill addresses issues concerning diplomatic relations with Taiwan. The bill directs the Department of State to seek to enter into negotiations with the Taipei Economic and Cultural Representative Office (TECRO) in the United States to rename its office in the District of Columbia as the Taiwan Representative Office in the United States. (The U.S.-Taiwan relationship is unofficial, and TECRO is Taiwan's principal representative in the United States.) In addition, the bill establishes a W nonimmigrant visa for aliens affiliated with Taiwan's diplomatic operations, including (1) an ambassador, public minister, or career diplomatic or consular officer accredited by Taiwan and accepted by the United States; (2) a designated principal representative of Taiwan to an international organization; and (3) the immediate family members of such individuals. Specified holders of a W visa shall be entitled to certain immunities afforded to holders of diplomatic visas. The bill also requires the President to appoint the Director of the American Institute in Taiwan with the advice and consent of the Senate. (After the U.S.-Taiwan relationship became unofficial, the United States conducted relations with Taiwan through the American Institute in Taiwan. The institute's office in Taipei performs many of the same functions as an embassy.)