It's funny how often this comes up. I really think the manual entry should be amended to include these details.
If you use NW, local storage goes to the "OS:\Users\Username\AppData\Local[i]AppName\Local Storage" folder.
I've only tested this with one game that uses local storage for a high score table, but I tested on five very different Windows-based machines and they all worked perfectly. Not once did I get a permissions popup or anything funny like that.
Is is 100% safe to assume that it'll always work on every PC in the world? I wouldn't be able to make that claim, but I've yet to see a complaint on the forums about NW-based local storage simply not working due to anything other than mistakes by game creators themselves.
Alternatively, there was a thread that came up recently about creating a custom file saving system, which you might want to look at if the stock options worry you.