How to move my city in this game?

Some events such allow you to move your city for free to certain specific locations but in general to move your city you need a teleport item. Random teleport items will send you to a random location in your current state. Advanced teleport items can be used to move to a location that you choose.

Teleport items are awarded as rewards for various challenges and activities but can also be bought for diamonds in the Item store or Alliance contribution points in the alliance store.