The most notable idea associated with Plato is that he thought philosopher-kings should run the government. Plato believed that the most knowledgeable and wise individuals, particularly philosophers, were best suited to lead and govern society, as they possess the understanding of justice and the greater good. This concept is famously outlined in his work "The Republic."
While Plato did tutor some prominent figures and faced significant challenges in his life, including living in a complex political landscape, the idea of philosopher-kings is central to his philosophical contributions.