Hi Julia,
I'm not sure about unsubscribe time, but you should be able to include "unsubscribe date" in your smart list. Try this:
1) Go to your Smart List.
2) Click on the "Leads" tab next to the "Smart List" tab.
3) Near the top-left corner, click on "Vew: Default" to open the drop-down menu.
4) Select "Edit Default."
5) In the pop-up window, use the "Find" search field for "Hidden Columns" and search for "unsubscribe."
6) One of the results should be "unsubscribe date." Select it, click the "Add >>" button, and then the "Save" button.
7) "Unsubscribe Date" should now be a visible column on your smart list that you can export.
Hope that helps.
-Alan