Where are quests in the menu?

Your main Tasks and Daily Tasks are found be tapping the message banner at the bottom of the main screen with the small book icon to the left (In your city) just above the chat bar.

If you are still in the tutorial phase of the game this will list the tasks to complete to move on.

The Events icon on the upper right will show any active events such as the Hourly Challenges, Clash of province etc.