In modern times the Queen of England visits former colonies like Australia and Canada quite frequently. How regularly did European kings and Queens visit the colonies back in the formative times of these colonies?
For England and her colonies, the answer is unfortunately quite simple. No English or British monarch ever visited the colonies in North America or the West Indies, before or during their reigns. During the settlement of Jamestown and Virginia, James I only even returned to Scotland once in his life (in 1617, Croft King James, p. 172). Charles came to the thrown in 1625, when Virginia, Plymouth, and St. Christopher had been settled. Over the next 17 years, Massachusetts Bay, Providence Island, Barbados were all settled but Charles never crossed the ocean. Neither James nor Charles ever even visited Ireland.
The same held true for the remaining Stuart King's and Queens - they were more likely to visit the continent than their colonies. Charles II planned to go to Ireland following his father's execution in 1649, but Cromwell's invasion and military success there deter him, and he instead goes to Scotland (Hutton, Charles II, pp. 34-35; Clarendon, History of the Rebellion, 1888 ed. 5:64, 102-105). James II did flee to Ireland following William of Orange's (later William III's) invasion of England. But rather than being there on an official visit, both were trying to raise support for an invasion of England (Miller, James II, pp. 220-222).
All this to say, that it was almost unheard of for monarchs to visit their overseas holdings. No French King saw Saint-Domingue, Martinique or Canada, no Danish King set foot on St. Croix, St. Thomas or St. John. The only major move that a European monarch made to the New World was when the entire government of Portugal relocated to Rio de Janeiro. In 1807, Maria I of Portugal fled Lisbon due to the invasion of Napoleon and relocated her court in Rio (Russell-Wood, The Portuguese Empire, pp. 25-26; Manchester, "The Growth of Bureaucracy in Brazil, 1808-1821", Journal of Latin American Studies, 1972 pp. 77-83). The capital of the Portuguese empire remained in Brazil until 1821, when Dao Joao was able to return to Lisbon and reestablish the seat of his empire (Schultz, Tropical Versailles).