This is a single-serving style page that I’m working on:

The idea is: Typically when I want to call someone in another part of the world, I’d like to know whether or not it’s OK to call and not necessarily what time it is.

The “donuts” rotate counter-clockwise and the reticle at the top of each circle represents the current time. If it’s red then it’s likely too late to call that part of the world – they are probably sleeping. Yellow means it’s early or late and green means the day is in full swing.

The colors are not final, and the design will probably change. Does this seem useful to you?