Originally called the Colony in Schuylkill by its founders in 1732, and later the State in Schuylkill after the revolution, the Schuylkill Fishing Company is a club most famous for its Fish House Punch - a blend of rum, Cognac, and peach brandy. When founded, members were given titles such as Governor, Sheriff, and even Coroner, and membership is limited to 25 individuals at a time. It is America's oldest club and arguably the oldest men's club in the English-speaking world. This "august gentlemen's society devoted to escaping domestic tribulation, but also to cigars, whiskey, and the occasional fishing foray," was situated across the Schuylkill River from Philadelphia in what is now Fairmount Park. Many great Americans have been members, but perhaps the most famous is General Lafayette, who was granted membership upon his visit in 1825.
Though the Schuylkill Fishing Company was the first men's club, a club created by Benjamin Franklin would have possibly the most far-reaching impact of any 18th century Philadelphia organization. In 1727, the Junto was formed by Franklin amongst a group of 12 craftsmen to "debate questions of morals, politics, and natural philosophy, and to exchange knowledge of business affairs." The Junto wiki page has a great introduction to the idea, and a list of current Junto groups. As the colonies matured and the American Revolution fostered an independent American culture, the American Philosophical Society "for promoting useful knowledge" was formed (again by Franklin) and flourished as a direct descendant of the Junto. The wiki page and the APS website are great resources on the Society's history and philosophy. Today, membership in the Society alongside names such as Charles Darwin, Robert Frost, Louis Pasteur, and Thomas Edison is highly regarded. The society also "promotes useful knowledge in the sciences and humanities through excellence in scholarly research, professional meetings, publications, library resources, and community outreach."
The APS museum and house, located on 5th right around the corner from Independence Hall: