I have this same issue. I have tried re-saving the settings/permalinks and the same issue takes place.
Remotely, the site was sitename.com/
Locally, the site should be found at localhost/sitename.com/old_site/
However, when I hover over a link, such as about, I see the browser attempting to go to localhost/about/
****Update****
I’ve noticed that the links in the site work correctly. The improper linking to “localhost/about/” only happens with the menus….
Any thoughts?
