Yes I would say " I went back to the cafe the next day..." You could say "the same cafe" but that seems unnecessary as it it is obviously the same cafe.

It's not bad. 'a second day' sounds slightly odd to me. Perhaps 'the next day' or 'a second time'? Also, normally the clerk is the person sells you the coffee, and the barista makes it. In most places I've been to, the two are separate. It would probably be more correct to compare the barista, rather than the clerk. But that's me being picky - those are minor things.