I am searching for good games for my ps4 with good story.
For example Zelda BOTW is a really good game I enjoyed.
Confusing!
Do you want a game with a good story or good gameplay?
You said that zelda is a "Good game I enjoyed" why? The story (Which i whole heartily disagree on. Personally zelda games and story has never been much of a good thing.)
Do you want a game that plays like breath of the wild? Some have compared it to Bloodbourne/Dark souls series.
Personal experience, if you want a game with good story but no monsters, horror, or SKYRIM, I can't give any good suggestions. I played few myself and never really thought much of it. Metal Gear Solid 5 Ground Zeros/Phantom pain is too long, and even boring most of the time, and the story is taking a huge back seat. Most people who want good stories would play RPG games, and I only know of the Kingdom Hearts HD collection or tales of beseria, I guess nier automata thought I haven't played the latter two. Yakuza kiwami which I have played is supposedly have a story, good is subjective, I call it satisfactory, it could be better but i'm glad is not worst. Just didn't understand why so many characters have to die. I guess if you don't like that, Shenmue HD collection is your alternative (Though I can't suggest it from personal experience)
Sorry if I'm not much help choosing a game, best option I can suggest is maybe just try some demos, buy games on discount or get playstation plus and sample free games or increased discounts.