Games with decent gameplay and decent story

S.T.A.L.K.E.R.: Shadow of Chernobyl
(I recommend the free Stalker Complete mod - http://www.moddb.com/mods/stalker-complete-2009 and its SC Realistic Weapons add-on - http://www.moddb.com/mods/stalker-complete-2009/downloads/sc-realistic-weapons-add-on)

(I'm literally just going over my Most Played games and listing the ones that you didn't list. :P )

Darkest Dungeon;
XCOM: Enemy Unknown;
Recettear: An Item Shop's Tale;
Skyrim;
All the Hyperdimension Neptunia games (yes, they do have stories and they are hilarious);
Since you mentioned Infinite- Bioshock 1 and 2? :P
King's Bounty series;
Devil May Cry 3 and 4;
Valkyria Chronicles;
Red Faction: Guerrilla;
Might & Magic: Clash of Heroes;
The Talos Principle;
Portal 1 and 2;
All the Half-Life games;
Alan Wake;
SpaceChem;
Long Live The Queen;
Warhammer 40,000 Space Marine;
Bulletstorm.

Ok, since I'm really starting to push the idea of what constitutes a "story", here's a list of games with awesome gameplay but more or less no story, because when you're having fun "story" doesn't matter. :D

Terraria;
FTL: Faster Than Light;
Serious Sam series;
Orcs Must Die!;
Crimsonland;
One Finger Death Punch.

Bioshock 1&2
Wolfenstein: The Old Blood
Call Of Juarez Gunslinger
The Bureau: X-Com Declassified
Deadly Tower Of Monsters slightly cheesy 50's science fiction setting
Edit:
Metro 2033
Metro: Last Light

The Elder Scrolls: Morrowind. Very deep story line, rich lore-filled game world. Graphics are dated. You have Oblivion but not played it yet, ditto with Skyrim. Oblivion is worth playing. I love the Avernum series myself. Have played 4, 5 and 6, but again, graphics might be an issue for you...certainly plenty of story to go along with.

the banner saga
darksiders 1+2
mark of the ninja
portal
icewind dale
overlord
fallout 1+2+tactics
wizardry 8
jade empire
kotor 1+2

the whole batman franchise.

Witcher 3 but it was already mentioned. Shame every other game is inferior to it.

L.A. Noire
Dreamfall Chapters

ENSLAVED: Odyssey to the West http://steamcommunity.com/id/genkicoll/recommended/245280/
The Swapper http://steamcommunity.com/id/genkicoll/recommended/231160
Oxenfree http://steamcommunity.com/id/genkicoll/recommended/388880
Max: The Curse of Brotherhood http://steamcommunity.com/id/genkicoll/recommended/255390
The Vanishing of Ethan Carter http://steamcommunity.com/id/genkicoll/recommended/258520/
Deadlight http://steamcommunity.com/id/genkicoll/recommended/211400/
Tormentum: Dark Sorrow http://steamcommunity.com/id/genkicoll/recommended/335000/
Valiant Hearts: The Great War http://steamcommunity.com/id/genkicoll/recommended/260230/
Nihilumbra http://steamcommunity.com/id/genkicoll/recommended/252670/

EDIT: You'll probably like ENSLAVED and Max the most, based upon your comments in the thread. Also, since you like Symphonia, you might like Zestiria? I'm not sure, I've not played Symphonia.

Did anyone mentioned these ?

Portal
Portal 2
Mafia (even better than Mafia 2 you have played)
Sacrifice (older game, but still good)
Brutal Legend
Firewatch (decent game)
Hotline Miami / Hotline Miami 2
The Chronicles of Riddick: Assault on Dark Athena
This is the Police
SOMA (if you like genre)

This War Of Mine

I would like to add Quantum Break, finished it last night and it was a great game.

Mad Max maybe?

Blood Omen, Soul reaver, Soul Reaver 2, Legacy of Kain: Defiance

Decent gameplay, best story in the history of games.

SOMA
Call of Juarez: Bound in Blood/Gunslinger
Dead Space 2
Alpha Protocol (the gameplay can be a bit of a pain for some, but the writing is really solid)
Max Payne 1/2/3
Psychonauts
Brothers in Arms: Hell's Highway
the 2 actually good bioshocks
Condemned: Criminal Origins
The Darkness 2
Hotline Miami
Banner Saga
Dark Souls 1/2/3
Transistor
Deus Ex 1
LISA
Wasteland 2

The Cat Lady
Eternal Senia
Amnesia A machine for pigs (if you are into horror)
Assasssins Creed games?
Metro 2033 and Metro Last Light?

brutal legend, castle crasher, crysis, dead space, metro,

Nobody has mentioned Prey? How odd....

Castlevania Lords of Shadows 2 (I never played the first one, but it might be good too.)
Devil may Cry series.
Prince of Persia trilogy.

I found these 3 a lot of fun and very much focused on the storyline.

Liking a lot of what's listed but I have tried a lot of them, though there are a few I haven't