I live in DC and I have studied the history a bit. OTL, there were already two thriving cities on the 10 square miles when the Revolution ended. Georgetown, MD was the port town for all the farmers (and later, miners) on the Potomac watershed all the way up to West Virginia, and Prelate John Carroll had destined it to immortality as the site of the young nation's first Catholic university. Georgetown is on a slight hill, and free from swamps, although a bit geographically hemmed in. Alexandria, VA was the port town for the farmers in northeastern Virginia, and while the river itself was a bit swampy, the uplands had fine soil and spectacular views, which provided opportunities for an attractive young woman like, say, Martha Washington, to end up with claims to two of the nation's most famous plantations, Arlington and Mt. Vernon.
The trick is that Georgetown/Alexandria are located right on the fall line, which is as far inland as a wooden seaworthy vessel can travel. That guarantees a monopoly of sort on all the trade south of Baltimore, MD and north of Richmond, VA -- not a very large monopoly, but enough that a city of some sort is destined to be within the 10 square miles.