Just in passing, my own Windows Time service is set to "manual" and is currently NOT running. To keep my clock in sync via "atomic time" (every night at midnight, from tick.usno.navy.mil), I instead use an old 3rd-party product I've been using seemingly forever, named Clockwise
I know, it's not free (but I paid for it once, many years ago with Win98, and I've been using it ever since) and it's been in this form and working perfectly for many years, and it doesn't need any change really. It does exactly what I need from it... which is a very nice clock/calendar display, a world time display showing a user-defined set of cities and their times, event/alarm mechanism, etc.
Here's the "expanded" presentation (which I don't normally use, because it's larger than I want), which allows for a "second time zone" value to also be displayed simultaneously, along with "primary time zone" and UTC:
and here's the "miniature" presentation (which is what I use, placed in a corner of my screen):
Note that with "miniature" there is a minor cosmetic problem using Aero desktop on Windows 7 along with "125% medium" font size. The title bar is supposed to display the day of the week, which it DOES do for WinXP and for Windows 7/Aero as long as you use "100% normal" font size. I miss it, but it's going to be fixed by the author in a new updated version that is planned.
There's also a "hidden" presentation version, where it is simply not onscreen at all but nevertheless is running all the time (for alarms and events, and also to update the system clock at midnight... or whatever time you set it to do that).
World time presentation (4x3 by default, but you can change the matrix size and can set the cities in each cell to your liking):