Daylight Savings is tonight (those of you running or along the route of the LA Marathon tomorrow, plan accordingly), and since those American readers will be losing an hour, I'll only take six minutes of your time.
A Sporcle quiz ought to do the trick. All I need from you is the most populous city in each time zone. There aren't any cities on the list that are so obscure that nobody's ever going to get them. Some are hard as hell, but not unfairly difficult, so if you're enough of a geography buff, all the cities are rattling around in your head somewhere.
Now get to bed.