I understand there are a lot of factors to consider here, but would it be possible for material from the ship's destruction to fall to earth and cause significant damage to a city? What is a reasonable amount of time to pass for the debris from the destruction to hit the earth's surface? 

It is relevant that the ship was built by humans and in the far future, but the material, size, and manner of destruction are irrelevant as long as it is possible for debris from it's destruction to hit earth. Basically I need to know if it is possible for the ship to be destroyed in some way and in a fairly tight time frame (minutes to days, not months to years) have debris hit earths surface.

Material, Size, manner of destruction, as well as orbital altitude can all be modified to achieve the desired outcome.