This is often attributed to Socrates (which would mean that it's from something Plato wrote). It's a well-known mis-quote though: the passage doesn't appear in anything Plato wrote, and it's much more likely to have originated in the 1960s than in Ancient Greece.

/r/TextDetectives checking in

According to wiki, it is a paraphrase from [this passage] (http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0241%3Acard%3D986) of Aristophanes' Clouds, (which is spoken by the character of "Just Cause", not Socrates):

Wherefore, O youth, choose with confidence, me, the better cause, and you will learn to hate the Agora, and to refrain from baths, and to be ashamed of what is disgraceful, and to be enraged if any one jeer you, and to rise up from seats before your seniors when they approach, and not to behave ill toward your parents, and to do nothing else that is base, because you are to form in your mind an image of Modesty: and not to dart into the house of a dancing-woman, lest, while gaping after these things, being struck with an apple by a wanton, you should be damaged in your reputation: and not to contradict your father in anything; nor by calling him Iapetus, to reproach him with the ills of age, by which you were reared in your infancy. ... Yet certainly shall you spend your time in the gymnastic schools, sleek and blooming; not chattering in the market-place rude jests, like the youths of the present day; nor dragged into court for a petty suit, greedy, pettifogging, knavish; but you shall descend to the Academy and run races beneath the sacred olives along with some modest compeer, crowned with white reeds, redolent of yew, and careless ease, of leaf-shedding white poplar, rejoicing in the season of spring, when the plane-tree whispers to the elm.

The paraphrase is kind of a stretch, but there enough similarities to see it as likely the original source.