Wall Street certainly didn't have the significance it does today insofar as its connection with American financial institutions go.

Wall Street was originally the north end of the city of New York, going all the way back to the beginning of Dutch settlement. There was eventually a wall built across it (which may have given the street its name, though some scholars point out that its original population was probably made up largely of Walloon immigrants, which may also have been the source of the name).

Everything north of Wall Street was mostly farmland, although by the time of the Revolution, the city had expanded northward to about where the present City Hall now stands. Beyond that, there was a bit more development on the east side going toward the Bowery, while Greenwich Village and Harlem were their own separate little towns, outside the bounds of New York City.

This 1776 map should give some idea of what New York City was like at that time. Wall Street isn't labeled, but it's the street that dead ends into the words "Murrays Warf". Federal Hall, the site of Washington's inauguration, is labeled on the map as "J". Nearby Trinity Church is labeled "K".

There was a bit of symbolism in the site of New York City in general because the Revolution had officially ended on Evacuation Day--November 25, 1783. New York City had been occupied by the British through the duration of the war, and the war came to an end when the last of the British troops left the city, evacuating shiploads of Loyalists with them. Later that same day, Washington and his Army rode into town down Broadway from upstate New York, and the war was over. There was a big public celebration and then Washington and his troops had a weeklong party at Fraunces Tavern, culminating in Washington's farewell address to his officers (not to be confused with his Farewell Address at the end of his presidency).

At that time, the capital of the U.S. was in Philadelphia, but a few months earlier, a riot by Continental Army soldiers threatened Congress there over undelivered pay. The governor of Pennsylvania had refused to protect Congress, which is a big reason that it was decided the site of a permanent capital city needed to be outside the bounds of any state's government.

In the meantime, Congress moved out of Philadelphia to a couple of different temporary locations while a building in New York City was retrofitted to house Congress.

That building was the then-current New York City Hall. Almost a century earlier, the original New York City Hall under the Dutch (the "Stadt Huys") was sold off in the 1690s because it was too close to the shore and prone to flooding, nor had it been built as a government building. It was originally a tavern.

A new City Hall was completed in about 1700, and that building was at the corner of Wall Street and Broad Street. This building housed the city government until 1784 when the new U.S. government took it over. It needed to be retrofitted first, and once that was complete, City Hall was renamed Federal Hall, and Congress moved in, in 1785. (Incidentally, this building had also been the site of the Stamp Act Congress back in 1765 that petitioned the King against the Stamp Act, but in both cases, the building was chosen by Congress simply because it was the government building in New York City, and was thus the most suitable site in New York for Congress to meet.)

Because Federal Hall was where Congress met, George Washington took the oath of office outside the building. In the meantime, some Congressional advocates wanted to move the capital back to Philadelphia, which occurred in 1790. But due to the riot back in 1783, Congress during the Constitutional Convention had already determined that a permanent capital outside the bounds of any state government needed to be built, so plans for Washington D.C. were already underway--they just hadn't determined where it would be. George Washington himself never governed from there, though, because D.C. wasn't completed until after his two terms as president were over.

So Wall Street being the site of Washington's inauguration was more or less a matter of convenience. There was a bit of symbolism to New York City itself being the location of Washington's inauguration, due to New York being occupied by the British throughout the Revolution and being their base of operations. But Wall Street itself didn't have any particular significance, except that it was the site of the building that Congress was meeting in at that time.

After Congress left New York City in 1790, Federal Hall returned to being New York's City Hall, but a new City Hall was built and finished in 1812, and the city government of New York moved there. (City Hall is still on the same site, but the building has been updated several times since.) Federal Hall was then torn down, but it was rebuilt in the 1860s to honor its place as the first capital of the United States under the Constitution.

As for Wall Street's connection to the financial institutions of the United States, that came a little bit later. The city directory of New York of 1789 shows that the various occupants of Wall Street and Broad Street at that time weren't particularly connected to the financial industry.

The Buttonwood Agreement was signed by a bunch of traders in 1792 at the foot of Wall Street under a tree near the shore, and this agreement was the genesis of the New York Stock Exchange. Additionally, the Bank of New York was located at Hanover Square at the time of Washington's inauguration, and it didn't move to the corner of Wall Street and William Street until 1796. So by the time of the Buttonwood Agreement and the relocation of the Bank of New York, the U.S. government had already been gone from New York City for a couple of years. The connection to the financial industry would not have been in the minds of Americans at the time of Washington's 1789 inauguration, nor would Wall Street have held any particular significance to the Revolution, either. New York City as a whole, on the other hand, had been the last bastion of the British at the end of the Revolution, so the city itself did have some significance.

Sources:

The story of a street; a narrative history of Wall street from 1644 to 1908 by Frederick Trevor Hill

Manual of the corporation of the city of New York by D.T. Valentine

A sketch of Fraunces Tavern and those connected with its history by Henry Russell Drowne

A history of the Bank of New York, 1784-1884 by Henry W. Domett

"New Light on the Philadelphia Mutiny of 1783: Federal-State Confrontation at the Close of the War for Independence" by Kenneth R. Bowling

The old Stadt Huys of New Amsterdam : a paper read before the New York Historical Society, June 15th, 1875 by James W. Gerard