While I'm sure a British expert here can explain the specifics of that better than I can, I'd just like to make a little side-note to say that the summit-type diplomacy of leaders visiting other countries has been sporadic throughout history. Indeed, at the start of the twentieth century, it was not particularly common. When Chamberlain went to Munich in 1938, for example, it was seen as being a quite unprecedented move. Nor was the United States particularly quick to do it. President Woodrow Wilson travelled to Paris for the Paris Peace Conference in 1919. In doing so he became the first sitting president to leave the United States, and he was heavily criticised for doing so. In fact, he was very nearly impeached, as House Republicans argued that it was unconstitutional for the US president to be somewhere other than the US.

None of this directly answers your question, I'm afraid, but it probably demonstrates that "travelling diplomacy" was not especially common at the time.

As /u/mariner01 said such visits weren't exactly common outside of the 20th century. However although I assume you're talking about a reigning British monarch, there are two occasions off the top of my head when a member of the British royal family who went on to be King visited the United States.

The first was William IV, he visited New York City during the American Revolution while serving in the Royal Navy. During this period NYC was a Loyalist hotbed and the HQ of the British Army during the Revolution, so as such it wasn't a state visit and it certainly wasn't to visit the leaders of what would become the United States. However he was visiting Americans amongst others and it was an American city. George Washington actually approved a plan to kidnap him while he was staying in NYC but nothing happened.

The second royal figure to my memory was Edward, Prince of Wales (future Edward VII) who after touring Canada came south and visited Detroit, Chicago, St. Louis, Cinncinnati, Pittsburgh, Washington D.C, New York City and Boston amongst others, this time in 1860 on the eve of the Civil War. Now bear in mind this was less than 90 years since the end of the Revolutionary War, only 45 since the end of the War of 1812-15. Political relations between Britain and the United States were still pretty testy and the American view of the royal family was not the almost adoption of them that we see today but was still coloured by the anti-monarchism of the Revolution. Despite this his visit was a huge success, 50,000 people turned out to see him in Chicago (for reference Chicago's population in 1860 was 112,172 - although obviously people came to see him from outside the city limits) and similarly large numbers in New York City, only the Irish being recalcitrant in celebrating his visit. He met the mayor, was led up Broadway with the crowds cheering for him, state militia and New York firemen paraded around the streets and a special ball was held for him. All in all a great success and quite peculiar given the United States' dislike of monarchism and it's awkward relationship with the former mother country in the mid 19th century.

So while the reigning monarch didn't visit the States until '39, there is a history of the British Royal Family in the States.