Remus's preferred drink was Milk tea. 

He kept teabags with him since he traveled a lot and they are convenient to use instead of brewing the tea all the way. 

Also whenever he would be stressed such as during exams, he would be seen for hours in the library with an enchanted teacup beside him pondering over books.

Earlier in his Hogwarts days, his most preferred drink used to be hot cocoa brewed especially by Sirius Black. Sirius had learnt how to brew cocoa and coffee by Mrs Potter and it became his specialty. He would treat his friends to cups of hot cocoa frequently. However, after James Potter's death and Sirius's imprisonment in Azkaban, Remus had not touched hot cocoa ever since.