When working with Areas in MVC, it's important to understand that they don't correspond directly to physical folder structures within your project or the URL. To keep things organized, you can structure your files like this:
/Content/Public/Css
/Content/Public/Images
/Scripts/Public/
and
/Content/BackEnd/Css
/Content/BackEnd/Images
/Scripts/BackEnd
UPDATE
To further elaborate on why an Area isn't a physical folder-structure:
For example, if you have an Admin Area in your project, the default route URL is /Admin/{controller}/{action}, not /Areas/Admin/{controller}/{action} (although you have the flexibility to set up routes differently)
This means that adding a Content folder under /Areas/Admin and placing a CSS file there will not be interpreted correctly by Visual Studio if you drag and drop the file into your markup. The HTML generated would look like this:
<link href="../../Areas/Admin/Content/StyleSheet1.css" rel="stylesheet" type="text/css" />
even though the URL for the Admin area is simply www.mysite.com/Admin
This discrepancy can cause confusion about the correct URL for the Stylesheet:
www.mysite.com/Admin/Content/stylesheet1.css
or
www.mysite.com/Areas/Admin/Content/stylesheet1.css
It's all a matter of perspective, but that's my take on it :)