How many goodly creatures are there here!
How beauteous mankind is! O brave new world
That has such people in't!
Prospero:The Tempest Act 5, scene 1, 181–184
'Tis new to thee.
Exiled from Milan, the former duke Prospero and his admirable fifteen-year-old daughter Miranda have been stranded for twelve years on an uncharted isle in the Mediterranean. Miranda's entire experience of mankind has, until very recently, encompassed only her bitter old dad and his deformed slave Caliban [see THIS THING OF DARKNESS].
After reading up on white magic, Prospero succeeds in ship-wrecking his old persecutors on the island and, after sufficiently humiliating them, produces them for his daughter's inspection. Miranda, trusting first impressions, finds these new "creatures" "goodly" and "brave." By "brave" she doesn't really mean "courageous," but rather "handsome" and "noble." Their wrecked ship had struck her as "brave"; her new fiancé Ferdinand looked pretty "brave" too; the whole pack of Italian princes and courtiers (most of them villains) are thus also "brave." Prospero has seen their inner workings, and knows how old this new world is, and how far from brave.
The phrase "brave new world" was your ordinary, not-terribly-quotable Shakespeareanism until Aldous Huxley put it on the map with his 1932 novel, Brave New World.