Where is the downloaded asset directory ?

It is located in hidden folder(Documents and Setting > Application Data > Unity).

I was looking for this as well. It also answered a few other questions I had, like: If an Asset is just a 3D model, how do I get to the model. I think the answer to this is: Open a new project with any 3D model selected as an included asset into the empty project then go into the created project folder and the 3D model file will show up there under assets then models. One could as well just create a full empty project then go to: C:/Users/(your user name)/AppData(hidden)/Roaming/Unity/Asset Store as stated in answers, include the asset into the empty project, again go into your saved project folder and all open 3D files from an included asset will be available to you. Good luck knowing which downloaded asset holds the files you are looking for. I found that hard myself, for there is little telling of what the asset has in it, other then the name of the asset it's self. My suggestion for that would be to create an empty project with most to all assets checked in the create empty project wizard, with a name like "opened-assets-project-v001" Then look for any and all 3D object file, as well as any other file like image, and C# files in the created project folder. Thank you to the one with the previous answer. I hope others find what I found out from it just as useful.

You have to create a new project then go back to Unity and import the asset to the new project.

There is a free tool in Asset Store can open the Asset Store packages folder https://www.assetstore.unity3d.com/en/#!/content/68761