The earliest theatres in New Orleans opened around 1813 and featured opera. Actors and musicians were brought to the New World to entertain New Orleans residents and visitors from very early on. It has been said that the tradition of touring companies in the United States can be traced back to the Theatre of New Orleans. You'll find this theatre company, and its troupe, mentioned in newspapers along the eastern seaboard from about 1830 onward.
While the history of the Mardi Gras is somewhat hazy, it may go all the way back to 1730. And some say the ethnicity of New Orleans is what gave birth to Jazz. Some trace the genre back to "La Bomboula-Danse Negre" composed in 1847. This work was the creation of Louis Moreau Gottschalk. His father was a Jewish physician who migrated from England and married a native New Orleans woman. The younger Gottschalk grew up in the French Quarter near Congo Square, the center of voodoo drumming and dancing. Research the history of Jazz and you'll find African Americans, Irish, Creole, Italians, and just about everyone getting in on the act. But the musicians who came on the immigrant ships were typically sailing on the smaller ships, as opposed to the larger vessels carrying great numbers of immigrants.
Some musicians and actors returned to Europe when their tour was over, so you might also find them on ships departing from New Orleans after the season closed. If you trace ancestors to Europe and then find them to trace, consider their occupation. If they were performers, they might have been traveling - and New Orleans could very well have been their destination from even the early 1800s.
Do a search for "actress" "history" "New Orleans" on Google Books and you'll find a wealth of information about performers. Switch "actress" for "actor" or "musician," and you'll find even more. Often their history tells where they were born as well as highlights in their career - including their travels.
While they are more difficult to trace, unless there was a stage mishap, there were stagehands, costumers, and all the behind-the-stage crew that would have been on hand in New Orleans, as well.
Browse through diaries and you're likely to find notes about ancestors who attended these performances, which is even more fun. Above all, don't overlook the performers in New Orleans. They just might be the link you are looking for.