I can't speak for executive orders for a mayor, but I can say that executive orders of the president are anything but symbolic. Their scope was expanded significantly under Bush and Cheney, and they are binding for federal agencies. For example, they used executive order 13440 to circumvent a supreme court ruling that stated the Geneva convention applied to the people they illegally kidnapped and held at CIA black sites. This EO functioned by essentially weakening the definition of torture, so they could go on and torture the folks they captured.

So, while the next president can just undo executive orders made by any previous one, making them a bit ephemeral, they do have direct and real consequences going as far as torture.