What were USA - British relations like directly following the American War of Independence? Did either side hold a grudge? How long did it take for relations to become friendly again? Did the founding fathers ever step foot in Britain after? I figure this question is fitting with the 4th almost here.
After the war the nations were trading and by 1785, John Adams was in England as an ambassador. The 1795 Jay Treaty is often credited with averting war between the US and Great Britain as it settled some lingering border issues among other things.
As for resentment and a grudge? Absolutely. The Jeffersonian Republicans wanted a closer relationship with France (who by this time had their own revolution) and opposed the Jay Treaty. The Federalists (Hamilton, Adams) wanted a closer relationship with Great Britain. The treaty was ratified, but only with exactly the two-thirds it needed and a lot of support from George Washington. In 1806 the Monroe-Pinkney Treaty was drawn up to continue the Jay Treaty, and the Jeffersonian Republicans wouldn't ratify it. This, among other reasons including the Jeffersonian support for Napoleon which Britain was fighting against, lead to the War of 1812.
Relations after that were unremarkable. There were border disputes between the US and Canadian territories. Great Britain chose to stay neutral during the Civil War (despite the Confederacy's hope that Britain would have helped them). Though Britain did build and launch the CSS Alabama that harassed US shipping - leading to a $15 million postwar arbitration settlement.
The relationship beings to change, in what is called the Great Rapprochement. Throughout the 1800s the British didn't really oppose the idea of the Monroe doctrine. Britain ultimately supported the US in the Spanish-American war, and the US supported Britain in the Second Boer War.
Relations moved closer with US support for Britain in World War 1 and 2, and has resulted in the now existing "special relationship" between the two nations.