To echo a bunch here:
Katawa Shoujo is really good romance and feels story (stories would be more appropriate as you have to play through all the girls paths to fully experience it) for a project that created by a group of dedicated 4channers off a single page of concept art. It follows the main character having to unexpectedly exchange to a school specifically catered to kids with disabilities and how he handles the sudden change and his relationship with the students there. Expect some meme worthy writing though in amongst the serious exposition and relationship development. Also some parts are nsfw if that's a issue but there is an option to toggle off the content but lose some pretty important scenes along the way. - PC but there may be a Mac version for it and Free.
The Zero Escape Series: 999, Virtue's Last Reward and Zero Time Dilemma are fantastic games with a mix of puzzles and story and I unfortunately I can't explain much about what the series is about without getting too spoilery. The basic premise is that Nine people are trapped against their own volition and are "encouraged" to engage in a game if they hope to escape. They're a little like the Ace Attorney Games in that figuring out who the mastermind is and why certain things happen are a constant logic puzzle you face but otherwise most of the gameplay is done through escape the room point and click style. - Wikipedia says it's available for PS4 and the whole series is on Steam. Make sure to play either 999 or VLR first as they can be played in any order and ZTD last or after VLR as it's extremely dependent on that game.
Steins;Gate is a fantastic story about time travel and it's effects but it's very devoid of gameplay and is more like DDLC than Ace Attorney. It's great if you want a story exploring a character and their relationship with their friends and how time travel critically changes their life and starts to affect their world view. Another play through all the paths to get the full experience. - Wiki says it's on PS4 and it's also on Steam. Also there's a sequel "Zero" but I haven't played it so can't comment on it.
The Danganronpa Series: Trigger Happy Havoc, Goodbye Despair, Another Episode, V3 Killing Harmony. It seems to be a very if you love it you love it or if you hate it you hate it series, there's no guarantee someone will enjoy, personally I did. Essentially it's a similar concept to Zero Escape: Group of people trapped at a local and have to engage in a game in order to escape (or will they?). In this case they are encouraged to engage in a killing game (basically Cluedo/Clue) where the killer will be let free if they manage to successfully kill someone and get off scot free after undergoing a trial (similar to Ace Attorney). The main draw is figuring out the mystery behind the killing game (why is it happening, who is the mastermind, etc) as well as the relationships between the characters and how they develop. Also the cases of course and the series pretty good musical score. Though you can miss out Another Episode as it's this 3rd person action shooter which isn't as great story or execution as the rest or really that interesting. Also if you want to get the full story of the first two games you'd have to watch the Despair (Prologue) and Hope (Ending) Anime of Danganronpa 3 (not to be confused with Killing Harmony). - On PS4 and Steam.
Psycho Pass is pretty Meh, wouldn't recommend it.
VA-11 Hall-A: Cyberpunk Bartender Action less visual novel, more bar fly simulator but still is pretty good. Haven't finished it yet but the characters and story is pretty interesting so far. Barely any gameplay though. - On Steam
If My Heart Had Wings is apparently pretty good but I've yet to play it.
Clannad is gut wrenching but amazing according to some but I can't say from experience.
Analogue: A Hate Story is pretty decent and interesting experience (bit like DDLC). - On Steam
And that's all I can think to recommend off the top of my head. Also if you're thinking of playing any of the Sakura "VN"s I don't really recommend it. There's a reason they're know for scantily clad characters and not much else.