Under the Continental Congresses and the Articles of Confederation the United States did not have a set capital city. The capital was considered to be any city wherein Congress congressed.
From 1774 onward to 1800 Congress met in Philadelphia (numerous times), Lancaster, and York, all in Pennsylvania; it also met in Baltimore and Annapolis in Maryland, and in Trenton and Princeton, in New Jersey.
In 1785, Congress began meeting in New York City, and continued to meet there after the new Constitution was adopted; officially, it is considered the first "permanent" capital city of the United States. George Washington was inaugurated on the steps of Federal Hall in lower Manhattan, officially considered our first "permanent" Capitol building.