Although time zone information is available online, I'm surprised that this isn't a feature in-game. It would be convenient to have that reminder pop up when you bring up the main menu.
If possible, Niantic could take it a step further by assigning a "ticket" when a player first begins playing during a community event. The ticket would not only display the time left in the CD/event, but count as their one-time access to the community event (preventing players from spoofing to access the event multiple times).