Shadow World

The Shadow World was a virtual simulation of Earth made by the Monks in order to prepare for a real invasion. (TV: Extremis)

Vatican
A virtal projection of the Twelfth Doctor was summoned by the Pope to go to the Vatican to investigate the Veritas. The Doctor, Bill and Nardole entered the Haereticum, from where Bill and Nardole found a room full of projectors, which led to another locations. (TV: Extremis)

Pentagon
One of the projectors led Bill and Nardole to the Pentagon, where a woman questioned if they had clearance for Floor 3. (TV: Extremis)

CERN
After leaving the Pentagon, Bill and Nardole ended up on CERN. (TV: Extremis)

Oval Office
After Nardole figured out he was also a simulation, Bill re-encountered the Doctor on the Oval Office, where the President had been dead for a number of days. (TV: Extremis)