Creating a public group

Out of the box, that group would be accessible to anonymous users.  You can verify the Everyone account has permission to view the Group under Manage Group > Permissions > Site Roles > Everyone.  The default would be to have the read permission in each application and the View Group Name in Lists permission.  If that is not the issue, there may be some other customization preventing access.

Thanks Mathew

I've got both of those permissions enabled but still no luck. It's weird because I have other open groups, and they are setup the same way. I'm definitely not seeing the woods for the trees on this one, anyway thanks for the help again Mathew.

Is it a Joinless group right off of site root?

It is yep

Is every page in the group requiring a login?  For instance the /b   /f    /w   pages?  

I've only got the one application, a blog and Everyone has permission to read blog posts.

But can you get to {groupname}/b  page?

No, that's behind a login, same as the group.

I'm a complete idiot Mathew. I missed the 'Read Group' permission for Everyone...

Welcome to learning it the hard way...I still do every day...