Does "within" have an antonym? If so, what?
Solution 1:
Mehper beats me to it with outside, so I'll just throw in a third alternative for the sake of completeness. Historically, without is an antonym of within, and Merriam-Webster still says that the first meaning of without is "outside" without further comment, but I don't actually see it being used that way these days. Wiktionary marks that usage as "archaic or literary".
Solution 2:
Outside is an antonym to within.
For example: Within or outside of an organization or institution.
Solution 3:
Outwith means outside of something.
Solution 4:
In Scottish English the antonym is outwith. I think it nicely resolves the problems with using without or outside, which often don't accurately reflect the intended meaning.
There's a picture of it on Wikipedia being used on a sign:
Solution 5:
I agree with "without." Reminds me of a Marx Brothers exchange:
"Without" is a broader term, covering both "lacking" and "the absence of," and also means "outside."
(This double meaning led to the Marx Brothers routine: "There's a girl waiting without." "Without what?" "Without food or clothing." "Well, feed her and send her in.")
From On Language, by William Safire.