The back story for my question is from this link here. I would like to keep in mind the musician may have knowledge of future events as they traveled back in time from the present.
Touring music in the 1500s would look very different than what you see today. You would rarely see groups do significant tours of any kind, because it was cheaper for the local Duke or King to hire a group of musicians.
You would, however, see composers being employed by Kings or Emperors, and brought to their city to compose or conduct for a while. Josquin des Prez (c.1450-1521), a famous composer of that time, traveled extensively between the courts of the Duke of Anjou, or the Duke of Ercole, among others.
Orlando de Lassus (c. 1532-1594) is another composer that travelled quite extensively. He was born in modern-day Belgium, but worked for the Medicis in Italy, the Duke of Bavaria, and others.
As far as the comment about touring independently as an artist, NOT under the employ of a noble, you would have a very hard time of it. Music tastes and schools were far more regional, and the average person wouldn't have the time or money to go to a musical performance. You would have to be hired by a noble, or by the church, as they would be the only ones with a venue large enough, and the means to pay you. The cultural differences would be the least of your concern.
Even 200 years later, when Mozart's father took him and his sister for their Grand Tour, they performed pretty much exclusively for nobles, palaces, and monarchs. The few times they did perform for an open audience, it was sponsored by the local nobleman, and touring was done by means of letters of introduction to contacts in that city.
http://staff.lib.msu.edu/sowards/balkan/lecture4.html
http://www.britannica.com/biography/Josquin-des-Prez
The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie. 20 vol. London, Macmillan Publishers Ltd.