At the time of the Revolutionary War, this house, known as the Hermitage, was much smaller and different than it appears today. It was built circa 1760, and some elements of the original construction remain. However, the house received major remodeling and additions in 1847-1848, and the original appearance of the house is uncertain. 
George Washington's Headquarters at the Hermitage - July 1778
During the Revolutionary War, the Hermitage was the home of British officer Lt. Colonel James Marcus Prevost and his wife Theodosia. James' military duties took him away from the house during the War, leaving Theodosia at the Hermitage. Although Theodosia was married to a British officer, she maintained good relations with American officers.
On July 10, 1778, two weeks after the Battle of Monmouth, George Washington and his troops were in North Jersey. Earlier in the day, Washington had picnicked at the Paterson Falls with officers including General Lafayette and Colonel Alexander Hamilton. Later that day, they arrived in Paramus, with the intention of making headquarters at the home there of Theodosia's aunt, Lydia Watkins. However, plans were changed when Washington received and accepted an invitation from Theodosia to stay at the Hermitage.  Her invitation read: 
"Mrs. Prevost Presents her best respects to his Excellency Gen'l Washington. Requests the Honour of his Company as she flatters herself the accommodations will [be] more Commodious than those to be procured in the Neighborhood. Mrs. Prevost will be particularly happy to make her House Agreeable to His Excellency."
General Washington and his staff arrived at the Hermitage later that day and remained here until the morning of July 15. Their stay appears to have been a pleasant one, judging by the following account written by Washington's aide-de-camp, James McHenry: 
"At Mrs. Provost [sic] we found some fair refugees from New York who were on a visit to the lady of the Hermitage; with them we talked — and walked — and laughed — and danced and gallanted away the leisure hours of four days and four nights and would have gallanted - and danced and laughed and talked and walked with them till now had not the General given orders for our departure. We left them however in the spirit of modern soldiership without much sighing in pursuit of the dangers of war and pleasures of variety."
Theodosia Prevost Marries Colonel Aaron Burr
James Marcus Prevost died in late 1781 after being wounded while serving in Jamaica. On July 2, 1782, Theodosia married Aaron Burr, who had served as a Colonel in the American army earlier in the war but retired from the army in 1779 due to ill health. 
Burr, who later served as the country's third vice president, was born in Newark and had connections to New Jersey which ran throughout his entire life. He attended school at the Old Academy in Elizabeth and the College of New Jersey (now Princeton University). The famous duel in which Burr fatally wounded Alexander Hamilton occurred in Weehawken. Burr is buried in Princeton Cemetery.