Where are the paths to the files open in Notepad++ (last open tabs) stored?

%APPDATA%\notepad++\config.xml

or perhaps

%APPDATA%\notepad++\session.xml

By the way, if you want to know how I found this out, I fired up Sysinternals ProcMon, set a filter on the ProcessName field to "notepad++.exe", closed Notepad++ and then ProcMon showed me which files had been accessed when I closed it.

This location should work regardless of username or Windows version:

%APPDATA%\Notepad++\session.xml

It's in C:\Users\<USER>\AppData\Roaming\Notepad++\session.xml