If a User is on a general page (i.e. not restricted), where should they go after clicking "Log Out"?
If a User is on a member-specific page (i.e. restricted), where should they go after clicking "Log Out"?
Not restricted - Back to the general page.
Restricted - A login page
Assuming the logout button is only there if they are logged in then you really have two choices - you either return them to the login page (or whatever page they were already on if that page doesn't require them to be logged in) OR you send them to a page that they can only get to when they log out.
I don't think it's a question of where "should" they go but more like where would you like them to go, and the choices are many: a thank you for visiting page, home page, a separate relogin page etc etc etc
I like logging people out to a 'Thanks for Visiting' page that generally has a nav to non-restricted access content on the site like home and Login.