Can someone give me the reasons why this comma cannot be skipped?
I am not sure where to go, though.
I find it natural to write this without a pause, but the word processor insists I use this comma.
When 'though' is used at the end of a sentence it is acting as an adverb modifying the whole sentence, and many style guides say the comma should go before it. Evidently your grammar checker obeys that 'rule'.
Your sentence must follow another sentence about going out, perhaps something like:
I really should go out. I am not sure where to go, though.
You could use 'though' as a conjunction instead and write:
I really should go out, though I am not sure where to go.
When used like this, the comma is optional.