can you expand on what you mean? Do you mean the accomplishments of Washington/the washington administration that can be traced directly to washington directly (versus say the stuff we primarily give various secretaries or ambassadors credit for) or are you asking what washington did on a day by day basis?
George Washington did several things as America's first president that helped build bridges and set precedent for future presidents to come.
First he was elected unanimously. There were many different opinions on how the fragile nation should function under this new constitution but the one thing everybody could agree on was that George Washington should be the head of the executive branch. This leadership was important in keeping a united nation.
Second is that he created the first presidential cabinet. There was nothing forcing him or telling him how to create a cabinet but he selected four men from differing viewpoints to work together for the good of the nation. It wasn't always peaceful or successful but it was a strong move towards unity.
As the first President he also set precedent by his actions. The state of the union address, the two term limit, presidential entertaining, and even the title Mr. President were all set forth by him. He was also delegated with the responsibility of appointing the entirety of the Supreme Court.
And finally, during his term, many founding bills and amendments were passed. The most significant of these would arguably be the Bill of Rights.
If you are interested about this time period, I'd recommend trying Empire of Liberty: A History of the Early Republic, 1789-1815 by Gordon S. Wood. As a piece of the Oxford History of the United States series, it has plenty of information.