While cleaning my computer, I notice that I have a lot of files that are marked as
LOCAL file under File type. Does anyone have a clue as to how to open these? My cleaning software is flagging these files as files that are junk files that need to be deleted. After looking further, instead of just deleting the files, it is because I have not set any file association to open these files with. Any one have a clue as to which program opens them? Any and all help is sure appreciated!:)

This is because Windows (stupidly) requires a file extension to know how to associate the file type (some other OSes don't do this, such as Linux/Unix).

There is no way to tell you what program should open these files because you may have a bunch of "local" files that are plain text and some might be binary. Some could be cookies, some could be cached images or what have you.

So in other words, if you try to open one of them up in "notepad" you may see some readable text, but if you tried opening another you might see all these black squares and weird characters. They aren't associated with a program because if they don't have an extension they can be files of any type/format.

It is likely that they are just cache files, cookies or some other sort of temp files.