Is the phrase 'to boldly go where no man has gone before' proper English?

Yes, it is correct grammatically. The only criticism it might get is the question of political correctness. Some people would object to the use of the Word 'man' in the phrase. I'm guessing that is why a later incarnation of Star Trek used "no one" rather than "no man."

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ROFL... I disaagree! denigrating the logical "man" of the era is as silly as saying the split infinitive is correct ... This phrase of Star Trek was actually "corrected"...

"To go boldly where no one has gone before" is, if I recall, how it ended up.

The improved cadence of the corrected infinitive was minimized by the silly vagueness of "no one" to replace "no man" in an era where intelligent females still were not offended. (They knew their self-worth and the millennia-old "discrimination" of ancient times has been contravened by able women for centuries.

But, the insecure among us tend not to research history, easy as it is becoming via the internet today.