We have already demonstrated how to migrate Public Folders to Exchange Server 2013 in our Screencast "Upgrade from Exchange 2007 to Exchange 2013"
It is not unusual to be in a situation where the organization you are upgrading to Exchange 2013 does not use Public Folders. Another common scenario is to have Public Folders that are not used anymore or, at least, you are assured they don’t need to be migrated.
Going through the Exchange 2013 Public Folder migration process does not make sense in this case. On the other hand, using ADSIEDIT to complete the upgrade without migrating the Public Folders is quite a barbaric approach and you are absolutely right to stay away from it.
In this screencast, we demonstrate how to complete the upgrade to Exchange 2013 without migrating the Public Folders. In addition, we show you how to copy the important ones (just in case) and how to re-create them later if they are needed by any chance.
For your convenience, we provide the text file with our project plan and commands that we are using in the screencast here