The Dragon Age franchise, especially Dragon Age Origins (plus Awakening expansion). In my opinion, DAO was a masterpiece. DA2 was rushed (they barely had 2 years to work on it), but despite its obvious rushed nature they managed to incorporate memorable characters, good enough writing for most of them (not all, though; then again that's subjective) and an overall pretty decent story (well... maybe except towards the end but again, it's subjective). DA Inquisition was overall decent, nothing horrible; but nothing quite that amazing. The main villain of Inquisition is extremely forgettable, and most of the game's companions are "meh" (some of them return from DA2), but the combat system of the game is probably overall the best one (I didn't have a problem at all with the more slow-paced combat of Origins but I can understand why Inquisition's combat fits more, and is simply done 'better' with dynamic combat in mind).
You liked Bioshock Infinite (me too, great game; although not as good as the original for me), so you shouldn't have much problem playing story-driven FPS games. Therefor I'd highly recommend Wolfenstein The New Order (not sure about the follow up the Old Blood spin-off / prequel, never played it; and I haven't played the sequel yet either). For some reason The New Order just didn't work for some people out there, oh well. I think it's one of the best story-driven single player FPS ever made (it could have easily been a movie). You might also like FEAR 1 & 2 (at least the first one), Crysis 1 & its "2nd campaign" game, namely Warhead (play as another character within the same events as the original game; seeing things from a different perspective... pretty much in the veins of Half-Life Blue Shift). Maybe going with Titanfall 2 wouldn't be far-fetched of a recommendation at all (it's actually a pretty solid game to be honest). I heard decent things about Singularity, but I never played it myself.
Finally, I'd recommend Star Wars: The Old Republic. However, things need to be taken into consideration for that one. I am recommending it because that game essentially offers the best Star Wars universe stories I've ever experienced since KOTOR1 and 2. The Old Republic has EIGHT 'base' campaigns, each one with 3 Chapters (4 of them for the Sith Empire, 4 for the Republic). They all lead to the more centralized expansions later on (Knights of the Fallen Empire / Throne). Now, Old Republic's writing for its main campaigns is - on average - pretty good. There's some absolute marvelous gems of moments (writing-wise) for various characters. The one campaign I enjoyed the most was for the Sith Warrior (although the Imperial Agent's campaign was very good as well, along with the Jedi Knight's). There's some campaigns I legitimately enjoyed even more than the movies.
The BIG PROBLEM, however, is the fact that Old Republic is... well, it's Old Republic. The game by now is VERY archaic, looks like the early days of WoW, has essentially no physics involved, has tab-targetting and a "combat system" that wouldn't fail to bore any sane person touching it (you REALLY have to not give a shit about excessively antiquated 1990s / early 2000s MMOs mechanics to enjoy that stuff to any extent). The STORIES and the characters development portion of the game is where Old Republic shines. It's basically Mass Effect meets Star Wars (I'm not exaggerating). You have your character, you have your companions (you find them one by one given specific circumstances), and your companions 'evolve' throughout the campaign (sometimes even in either good or bad ways depending on your decisions). It's definitely a 'formulaic BioWare game', for the best (since comparisons to Mass Effect and Dragon Age in how you acquire you companions and how the dialogue functions and branches out can be made). It's simply a recognizably-BioWare game. But... it's also an MMORPG. So... ALL the "In Between" stuff you'll do (between cut scenes, between actual story progression moments, between talking to your companions on your ship, between seeing your character evolve based on your decisions) is merely MMORPG shenanigans.
So you'll be doing mostly meaningless side quests (I say "mostly" here because there ARE some side quests that have very good writing and have pretty nice and short isolated stories on their own scattered across most planets; but there's not hundreds of them). The most boring and difficult thing to get over (for me anyway, it was) is the combat system, and character animations in general. It's excessively harsh to look at, and play with (I absolutely hate tab-targetting and enemies that just stick on you, where physically moving won't change anything to auto-aiming and guaranteed shots; it's very old by today's standards, and that's putting it gently). Additionally, a major annoyance (to say the least) is traveling and back tracking to reach Point B and then going back to Point A, then being told to go to Point C, then back at Point A... (while doing quests) on planets. The distances are sometimes VAST, with vehicles that move about as fast as I can walk; making the whole 'doing this quest to get rid of it so that I can see what's going on next in the Story' a chore in most cases. There's some campaigns (notably, Sith Inquisitor's, towards the end for example) where at some point you'll literally be spending about 30 minutes on planets, on your ship, then back on new planets and then back on your ship doing backs and forths to 'progress' your story in the worst possible manner. There's genuine horrible quest pacing and planning (I.E. the devs didn't plan on balancing how much "gameplay" goes in between portion 'x' and 'z' of story progression, making certain quests over-lasting just to end up getting a 2 minutes cut-scene only to then being told to go on another mission again that lasts a solid 20 minutes with back and forth traveling AGAIN) on the part of the devs in many places.
I always hesitate to recommend Old Republic due to those reasons (and then some; the graphics in general, too, are nothing spectacular to look at nor were they even back when the game was released). However, I still do... since the game does have gems of characters and writing. It simply was a mistake to combine MMORPG with 'Campaigns'. The game, on a side note, CAN be played entirely Solo for just progressing the campaigns (you don't have to do Raids, or anything with people if all you want to do is experience the game's stories and campaigns). But they throw in MMORPG fueled mechanics and quest progression (and pacing) that just don't fit both formula at the same time. It's not an easy one, it's probably not for everyone but... the stories (in general) alone still make it one of the best game I can recommend for the Star Wars universe if what you want to experience are story-driven games.