The British had to evacuate most of them because of fears of postwar reprisal. This was no easy task because there were far more loyalists than we tend to imagine. In fact during the war there had been more armed loyalists (including freed slaves and Cherokee Indians) fighting for the British side than regular British army soldiers engaged in the conflict as well as more fighting loyalists than the entire strength of the Continental Army.
After the war these tens of thousands of loyalists became refugees because they lived in real fear of American reprisal. The new American government explicitly intended to re-enslave blacks who had fought for Britain and expropriate some amount of loyalist property. The Revolutionary War had been characterized by irregular mob violence against loyalists, especially tarring and feathering, so loyalists lived in fear and demanded that Great Britain protect them by offering them land elsewhere in the Empire.
While the Treaty of Paris was being negotiated loyalist refugees nervously waited in port cities that remained under British control, like New York. In New York alone 29,000 loyalists were evacuated on British ships before the city was handed over to the Americans. So where did they go? Many places within the British Empire, depending on who they were. The largest number settled in Canada, including many freed blacks, others who owned slaves went to Spanish Florida or the Bahamas. Many ended up living out modest lives in Great Britain, but were able to see their children educated and set them up careers in the military or colonial service. Former slaves who had emigrated to London, and found themselves unwelcome there, were the founders of the colony of Sierra Leone, a project established for the relief of the "Black poor"
Overall between 50,000 and 100,000 loyalists left the new United States to settle elsewhere in the British Empire. They had quite an impact on the places they settled as well as a changing concept of British Empire in the aftermath of losing the American colonies.
A great book on this subject is Liberty's Exile's by Maya Jasanoff. Jasanoff is a genius and sure to be the next big name in British history.
I can't tell you about all the loyalists, but I can tell you about some. So the British army promised freedom for any American slaves who chose to fight for the British. After the British lost they were mostly sent to Nova Scotia and later to Sierra Leone in 1792.
Simon Schama Rough Crossings
Often referred to as United Empire Loyalists, many fled to Canada. Those who stayed often suffered a variety of misfortunes.
"At Quibbleton, New Jersey, Thomas Randolph, cooper, who (as the Patriots said) had publicly proved himself an enemy to his country, by reviling and using his utmost endeavours to oppose the proceedings of the continental and provincial conventions... was ordered to be stripped naked, well coated with tar and feathers, and carried on a wagon publicly around the town - which punishment was accordingly inflicted. As soon as he became duly sensible of his offense, for which he earnestly begged pardon, and promised to atone, as far as he was able, by contrary behaviour for the future, he was released and suffered to return to his house, in less than half an hour,"
Source: A Short History of the United Empire Loyalists by Ann Mackenzie M.A. http://www.uelac.org/PDF/loyalist.pdf .