In a scenario where you are reporting an event where someone came to your house which of these two sentences is appropriate, " he came to visit me yesterday” or "he came and visited me yesterday.”
Either one is correct. He came and visited is less formal than he came to visit. If you are reporting the event in the formal sense ("reporting an event" sounds pretty formal) then use he came to visit or just He visited me yesterday. If you are just talking about your day yesterday to someone (less formal) then you could use either one.
I would prefer "he came to visit me" or simply "he visited me" in all registers, formal or informal. But there is nothing at all wrong with "he came and visited me" -- the difference is a matter of style. This google ngram indicates that the "and" form is much less common (in the corpus that google uses). This alternate ngram indicates that "he visited me" is significantly more common than either alternative.