The modern American "steakhouse" is largely a development of the mid-19th century, developing especially in New York and later in Chicago. The oldest continuously operating steakhouse in the United States is the Old Homestead (in Manhattan) but Palm's and Peter Luger (in Brooklyn) are also nearly as old.

The New York Times wrote an article about this back in 1994: http://www.nytimes.com/1994/01/21/arts/for-red-meat-and-a-sense-of-history.html?pagewanted=all

As the article discusses, the way beef is "aged" has changed -- most beefsteaks these days are wet-aged in vacuum-sealed plastic containers, and dry-aging for more than a few days is quite rare. In the late 19th century, whole sides of beef were functionally dry-aged as they spent a week or more being shipped in refreidgeated rails cars from Midwestern meatpacking plants to markets on the Eastern Seaboard.