The verb is "go up to", not "go up" up to = towards something that is over there Walk up to the house. (The house is over there.) Run up to the tree. (The tree is over there.) Look up to the moon. (The moon is up there.) Look up to the teacher. (The teacher is a bit smarter.)

You cannot use "Go up to something" in every context. When someone walks up to something or goes up to something/someone, the person needs to be in close proximity to the subject in the sentence. "As she was standing by the house of her childhood observing it, she noticed that there was actually someone inside it. She came up to it to take a closer look." "When she looked to look at him, he was already walking towards (up to) her from the other side of the room" Basically, it's the same verb of going, or walking, but you are simply adding "up to" indicating that the person was in close proximity.

Up is used as a direction term. Like a proposition, it tells her position- from where she was to over by the house. You can go up the road - path - street - up bedside - up the hill and more. It is much like saying "went, going, go over to" or it is like saying following the- path - street....." It can- but does not need to mean higher altitude.