To abandon a city, select Abandon City from the bottom of the Town Hall menu. If you only own one city, there will not be an option to abandon your city. You can instead restart your account by clicking Options>Account>Restart Game. You will start at a new location with a three-point city. You cannot restart within the first 40 hours of play, and you cannot restart again for seven days.
Abandoning or manually restarting requires an abandon code that will be sent to your registered email for security purposes. The abandon code can be used for multiple cities within the same 24-hour period. When you abandon or restart, you will keep your title. (It’s impossible to lose your title.)
If all of your cities are destroyed, you will be restarted. There is no need for an abandon code in this case.
If you don’t play on a particular world at all for 14 days, your game on that world (and only that world) will be deleted. There is no other way to delete a game other than closing your account which will affect all worlds.