An extensive profile of NSA Chief Keith Alexander by Shane Harris of Foreign Policy mentions an "Information Dominance Center" in Fort Belvoir, Virginia that was designed to look like the 'Starship Enterprise' spacecraft from Star Trek.

As commanding general of U.S. Army Intelligence and Security Command (INSCOM) from 2001 to 2003, Alexander oversaw the Trekkie setup and used it to woo policymakers.

From Foreign Policy:

... Alexander brought many of his future allies down to Fort Belvoir for a tour of his base of operations, a facility known as the Information Dominance Center. It had been designed by a Hollywood set designer to mimic the bridge of the Starship Enterprise from Star Trek, complete with chrome panels, computer stations, a huge TV monitor on the forward wall, and doors that made a "whoosh" sound when they slid open and closed. Lawmakers and other important officials took turns sitting in a leather "captain's chair" in the center of the room and watched as Alexander, a lover of science-fiction movies, showed off his data tools on the big screen.

"Everybody wanted to sit in the chair at least once to pretend he was Jean-Luc Picard," says a retired officer in charge of VIP visits.

Glenn Greenwald of The Guardian found what appears to be photographs of the 10,740 square foot headquarters on the website of DBI Architects, Inc. (which is "currently experiencing a high volume of traffic").

The brochure reportedly boasts that "the prominently positioned chair provides the commanding officer an uninterrupted field of vision to a 22'-0" wide projection screen."

The view from the chair: And here's the meeting room: