I like traveling while my best friend prefers 【being 】at home.
prefer doing sth.更喜欢做某事
整句翻译：我喜欢旅游,然而最好的朋友却喜欢呆在家.
2.It is best to go out of our way 【 to make 】some western food for our visitors
不明白的再问哟,请及时采纳,多谢!It is best to go out of our way＿＿＿(make) some western food for our visitors