Although the White House website states that tours for non-U.S. citizens can be arranged through their respective embassies, the requirements for access to the White House by foreign nationals are such that visits of Austrian citizens will unfortunately not be possible for the time being. U.S. citizens can still apply for tours through their respective member of Congress.
The Embassy recommends to visit the White House Visitor Center instead (1450 Pennsylvania Avenue NW between 14/15th Street NW). Alternatively, the U.S. Capitol can be visited at no charge. Guided tours can be booked in advance.
Furthermore, most museums in Washington, D.C. do not charge admission, cover a variety of subjects, from art to air and space and are mainly located on the National Mall (Metro accessible through the stops “Smithsonian” or “Archives”).
Tours of the Pentagon have to be booked individually through the Pentagon website. The Embassy cannot assist in the booking process of Pentagon tours.