"This public service is cooperatively provided by the two time agencies of the United States: a Department of Commerce agency, the National Institute of Standards and Technology (NIST), and the U. S. Naval Observatory (USNO). Readings from the clocks of these agencies contribute to world time, called Coordinated Universal Time (UTC). The time maintained by both agencies should never differ by more than 0.000 0001 seconds from UTC."
This website includes some exhibits on the history of timekeeping, the history of calendars, what is an atomic clock, informaton on daylight savings time, and information on quartz watches.
http://tycho.usno.navy.mil/what.html Time from the U.S. Naval Observatory Master Clock.
http://tycho.usno.navy.mil/simpletime.html Time in the U.S. time zones from the U.S. Naval Observatory Master Clock.
As for the time information for major cities from around the world, I've found that this non-governmental website provides accurate and reliable information. http://www.timeanddate.com/worldclock/ It also contains links and applications for stopwatches, calendars, date calculators, moon calculators, information on eclipses, time zone information, etc.