[This map](https://www.worldtimezone.com/) is a very interesting site for looking at the current time in different time zones around the world. It's useful for finding the relative time in different locations but you don't need to search through a list or select cities from a drop down. It's probably best to go from the [sitemap](https://www.worldtimezone.com/sitemap.html) rather than trying to navigate the pages though. I found this when I had the idea for a web app which is a map that you can scroll around/zoom into and you can place virtual clocks by clicking. Then as you zoom out you can see the clocks on the world map for the places you've selected. This should accomplish most of that functionality.