In this case it's 游 which specifically refers to "fun", there are also broader terms like 旅行 that refer to a general travel itinerary, but 旅游 to me feels like the most common conversational term for "travel" (i.e. the only one I understood well as a kid)
旅游 and 出差 » interesting, i assume it's not a case where there's a general "traveling" that kinda covers both
In this case it's 游 which specifically refers to "fun", there are also broader terms like 旅行 that refer to a general travel itinerary, but 旅游 to me feels like the most common conversational term for "travel" (i.e. the only one I understood well as a kid)