How does the Golden Age (Renaissance) affect America today?

In American history, there are two Renaissances that are significant: the period of literary production called "the American Renaissance," which occurred between the 1830s and the 1850s, producing its most significant works between 1850 and 1855; and the Renaissance in Europe, which is usually referred to as "the Golden Age." Because of your emphasis on "the Golden Age," I will assume that you are talking about the European Renaissance.
The Age of Exploration, which coincided with the Renaissance, led to the European discovery of what they termed "the New World." While explorers from Portugal and Spain (Columbus was Italian, but funded by the Spanish monarchs Ferdinand and Isabella) sailed around the Americas and Africa, artists—particularly in Italy—were reviving Classical traditions in painting, sculpture, and architecture. This revival would be repeated once again in the eighteenth and early nineteenth centuries during the Neoclassical era in art, which came after the French and American Revolutions. The influence of Classical architecture is seen everywhere in the US but particularly in the designs of Monticello and nearly every building and monument in Washington, D.C.
The influence of humanism is also still felt. Humanism is the belief that most of the world's problems can be solved by rational thinking and that civilization (e.g., arts, technology) is a great human achievement and ought to be the goal of most societies. We have retained this view, though Western biases, which we can trace back to the Renaissance, have limited our ideas about what civilization can look like.