Well, it doesn't get much more in my wheelhouse than this.
The War of American Independence did not, as you noted, end after Lord Cornwallis surrendered his army at Yorktown. Instead, Yorktown is best understood as the beginning of the end.
The most immediate impact of the British losing another major (and previously successful) army in America was the collapse of Britain's pro-war government headed by Lord North. North's blunderings had helped cause the war in the first place, and he had never managed to formulate a policy for winning in North America. Despite this, North enjoyed the full confidence of King George III. The defeat of Cornwallis, who had campaigned across the entire South without a true battlefield defeat (Guilford Courthouse was, at worst, a draw), proved that British military victories were meaningless without a the ability to firm up the political loyalty of the colonies. If there hadn't been a loyalist uprising in the most theoretically loyalist colonies when the British were winning, there certainly wouldn't be one now that the rebels had captured another army. Cornwallis' capture meant that the Crown would need to raise and deploy another army to North America, without any clear prospect of victory and while also fighting the French, Spanish, and Dutch across the world. It was time to sue for peace. Parliament held a vote of no confidence in North on 20 March 1782, which North lost.
Lord North was succeeded by Lord Rockingham, an outspoken opponent of the war and friend to the most radical members of Parliament. Lord Rockingham appointed one of Parliament's most pugnacious liberals, Charles Fox, as one of this two Secretaries of State. The king HATED Fox (and to a lesser extent, Rockingham), and toyed with the idea of abdicating the crown rather than give his assent to any government formed with Fox in it. George III ultimately relented after Rockingham added the comparatively more moderate Earl Shelburne to the cabinet as a second Secretary of State. Shelburne had a very clear price of admission into the cabinet: he would only serve if the king recognized American independence and end the war. Rockingham lived just long enough to form his government, dying on 1 July 1782.
Being that George III would never assent to any government headed by Fox, Lord Shelburne replaced Rockingham as prime minister. Fox resigned in frustration, and eventually formed an unlikely alliance against Shelburne with none other than his hated political foe, Lord North. The Shelburne ministry lasted just long enough to negotiate peace with America and its allies and extract Britain from the geopolitical/military jam North had steered Britain into. Shelburne's representatives at the Paris peace talks offered the Americans such generous terms that they broke off and signed a separate peace, dragging France and Spain into a signing a treaty before they were truly ready (more on that later). The borders of the United States would extend from the Atlantic to the Mississippi, and from the St. Lawrence/Great Lakes to the Floridas (returned to Spain from British control; Britain had received East and West Florida from Spain at the end of the Seven Years War in exchange for Britain returning Havana, Cuba to Spain after the British captured the sugar port late in the war). Between the defeat of Cornwallis in October 1781 and William Pitt the Younger 's appointment as Prime Minister in December 1783, Great Britain had 5 prime ministers and at least two instances where the king quite seriously considered (or threatened) abdication.
With all this political chaos, Britain was understandably reluctant to undertake major offensive action in North America. Sir Guy Carleton commanded the largest remaining British force in America, around 10,000 men in New York City. After Yorktown, Washington reunited the forces he had taken to Yorktown with the large garrison force he had left in the Hudson Valley, bringing his total number of troops to around 10,000. Military commanders hate a fair fight; the two armies settled into their respective bases and skirmished occasionally while waiting for their governments to sign a peace treaty.* News that the parties at Paris had signed a peace treaty started to reach North America in late February 1783, and Congress accepted the terms their representatives had agreed to in early April. Washington announced a cease-fire to his army on 19 April 1783. The British evacuated New York City on 25 November 1783.
Up until the British left New York City, Washington was concerned they would resume the offensive against him. The American authorities never lived up to the stipulations of the treaty regarding fair treatment and compensation for those Americans who had remained loyal to the Crown, giving the British cause to declare the treaty a dead letter. The officers of the Continental Army nearly mutinied in March 1783 over Congress' failure to give them pensions and back pay, and several enlisted mutinies broke out after the ceasefire as men enlisted for the duration of the war felt that they were being held beyond the extent of their enlistment contracts. Washington was able to placate the officers with a pretty good speech and a bit of theatrics, but had to send the "for the war men" home early to avoid a general mutiny, All of these crises, particularly furloughing home nearly half the army, provided an opportunity for the British to attack, but they fortunately (and wisely; nothing would heal a rift in the army like the enemy perfidiously attacking despite the forthcoming treaty) they opted not to.
The Americans were fortunate Shelburne was such a staunch opponent of the war, as the British did much better against the French, Spanish, and Dutch after Yorktown. Fighting in the Caribbean swayed back and forth (the Spanish recaptured the Floridas, but the Franco-Spanish fleet never managed to launch an attack on Jamaica like they hoped). In Europe, British forces held Gibraltar against a siege that lasted four years, eventually sortieing out to torch the Spanish floating batteries and break the siege in 1783. In India, British forces roughly handled a French fleet and the French-allied Indian kingdoms it was there to support, strengthening Britain's hold on the subcontinent. There was an argument to be made (and was made, by North and the other conservatives in Parliament) that Britain should ignore America and keep fighting the allies around the world.
In summation, the years after Yorktown were both politically and militarily important to the American Revolution, and saw several moments when events could have taken a radically different turn. The failure of the British military to find a way to win in North America and political uncertainty were the two biggest reasons why the British did not commit to another offensive against the United States even as the nascent republic struggled to find its footing and its allies lost ground to British arms around the world.
Sources
Thomas Flexner, The Perils of Peace
William Fowler, An American Crisis
*This is not to diminish the fighting that occurred during this "quiet" period. Among the more famous causalities of this skirmishing was Private Robert Shirtliff of the the 4th Massachusetts Regiment, who was wounded in the leg by a buck-and-ball round (one cartridge loaded with a musket ball and 4 rounds of buckshot) fired by a loyalist. Shirtliff was actually a woman - Deborah Sampson of Middleborough, Massachusetts, discovered only after she caught a fever weeks before the British evacuated New York for good. Sampson/ Shirtliff received an honorable discharge from the Army on 25 October 1783.