Is the opposite of 'within', 'without'?

Solution 1:

It appears that it can also be used in that sense, though less common.

without

• On the outside: a sturdy structure within and without.

The Online Etymology Dictionary has reference to your issue.

without (adv., prep.) Old English wiðutan "outside of, from outside," literally "against the outside" (opposite of within), see with + out (adv.). As a word expressing lack or want of something (opposite of with), attested from c.1200. In use by late 14c. as a conjunction, short for without that.

within (adv., prep.) Old English wiðinnan "within, from within", literally "against the inside", see with + in.

Solution 2:

There is a hymn that starts with the words, "There is a green hill far away, Without a city wall." Here the word without clearly means the opposite of within. It is archaic but it certainly used to be used in this sense.