If in a situation of privilege, travel was not troublesome. Even as late as the 1930s, upper class travelling would be accompanied by letters of introduction to relevant peers. European nobility had far reaching contacts all over the globe, as Foreign Offices and Embassies were commonly staffed with aristocracy. However, for women travel of this sort was considered far more restrained, as in many countries commoner women could not travel alone without proper paperwork by a man allowing them to do so. (Some brave women of course did nevertheless, against much daily hassle.)
Crossing borders as such was not generally speaking a problem: passports existed, tourism had begun (at least in Europe) in the immediate aftermath of the Napoleonic period; nobility, but also artists, poets and adventurous citizens who could afford it would easily travel throughout Europe and many parts of the world in the 19th century, as is proven by the vast number of travel novels and reports from the period (something becoming very popular already by the late 18th century). Byron, Goethe, Shelley and many others traveled far and wide almost a hundred years before your time frame, and they weren't even particularly high nobility (but of course upper class) in any sense.