I would say that came up to means roughly the same as approached (that is, move into close proximity with):
She came up to the window and asked to buy four tickets.
whereas came to can be used to mean arrive at:
I remember the day the veterinarian came to our farm and brought the bad news.
Obviously, there is some overlap between the two, because when you move close to something, you are also arriving there. Because of that, I would say that you could always use came to, but you wouldn't necessarily always be able to always use came up to without a possible slight shift in meaning. For example, in my second sentence, if I were to say:
I remember the day the veterinarian came up to our farm and brought the bad news.
that might imply something different. It could imply the doctor walked up along the road and stood at the fence (as opposed to in the original sentence, where it's easier for me to imagine the veterinarian in the kitchen). Another possible interpretation after adding the word up is that the veterinarian came from further away – in other words: I remember when the veterinarian came up [from the city] to bring us the bad news.
However, if I said:
She came to the window and asked to buy four tickets.
that pretty much says the same as the original, because we approach a ticket counter in the same way we arrive at a ticket counter.
As a footnote, these usages don't include more idiomatic uses of came to, such as:
I heard the trivia question on television, but it wasn't until I was driving in my car an hour later that the answer came to me.
The boxer was unconscious on the mat for a few seconds before he came to.