Everyone keeps on saying the Last of Us, but it's by no means a perfect game (someone needs to be real here). Buy it if you want great story, but the gameplay isn't anything amazing. It's like Bioshock Infinite in that regard. Story that gets you, but gameplay that might get you... mad. Keyword is 'might'.
I'd recommend the Uncharted Collection (I've been wanting to buy it since it released) and the upcoming Uncharted 4 looks ever better. Those games are kinda like modern day Tomb Raider, but with much better story across multiple games. The mechanics might be iffy in the earlier games, but it's probably the best value for money PS4 title: 3 games in one.
Bloodborne is a killer app if one likes the Dark Souls type games, though it's not exactly the same as Dark Souls (otherwise it would have been called Dark Souls 2.5 or something). It's got a lot of interesting lore to boot too, a lot of that creepy Lovecraftian-type stuff.
Infamous Second Son (and I think there was another one) is a good action game exclusive to PS4. Muck around with superpowers and have fun.
If you like games like the Telltale games, you might like Heavy Rain Remastered. IMO, it's much like the Last of Us, but with less 'traditional' gameplay. Awesome story (it must be seen by all!), meh gameplay. It's like playing a movie. As for plot: it can be some pretty grim stuff, in the good kind of way.
Similar to that recommendation is Until Dawn. A highly acclaimed game of 2016, it's a horror game with those similar exploration/QTE elements and has a suprisingly charming story. It's great to play with friends, you can argue over timed decisions and if characters get killed. I watch the Scary Game Squad play this one and it was hilarious XD
Drive Club is the racing game, if you like that sort of stuff. It's a very good looking arcadey racer and great for multiplayer (the online sort, no split-screen).
If you didn't play Journey on PS3, it's the must-own indie title on the sytem (and also highly acclaimed, many people's GoTY when it first released). I won't spoil it, but it's short but sweet and there's a lot of feelings and meaning behind it. Probably the deepest game on this list.
If you like grindy MMO gameplay mixed with FPS (like the Division), then Destiny wil be right up your alley. Though it's best to find friends to play it with. I'd steer clear of it personally, mainly due to the way they are selling that game (DLC is literally required for the best experience). As many people say, year 1 was terrible, but year 2 got better. But then one long time Destiny player had
this to say.
If you even consider the Order 1886...
this.
I won't recommend many multi-platform/non-exclusive titles, since OP mentioned they are a PC gamer and are thus likely to have already played them, but Rocket League is a good shout, since it has cross-play you can play with your buddies on PC. Some games with abysmal PC ports like Arkham Knight have their best version on PS4.
Game to look out for in the future include Horizon Zero Dawn and No Man's Sky, but wait till they release.