Interlinking relevant company owned websites generally does not lead to penalties but it might not be the best use of your resources. Adding 60 office links to every page is probably not the best use of your link juice. Plus Google tends to devalue ROS navigation links. I would try to build the links to your local offices into relevant content. When you post an announcement about a new building project in Syndney, make sure to link to the Sydney office from within that announcement.
I also don't understand why you didn't fix the problems with the two main sites instead of launching 60 new sites. That makes me think you might have been looking for a shortcut. Admittedly I used to do shortcuts of launching mini-sites and it used to work great. Now it is generally better for long term profits to build a big site with good quality signals for Google to see. You can debate the many pros & cons of running a big site vs. 60 local mini sites.