Name of a board game with a world map and an airplane traveling to different cities
Your memory of the game's name is pretty much correct,
The game in question is called "Holiday!"
(note the !, as there is another game called "Holiday" that is quite different to what you remember).

The rules to "Holiday!" are almost exactly as you remember, with the addition that the destination cards also hold a day of the week, which awards a player additional points for reaching the destination on that day.