if you haven't played it you should definitely get GTA5 and The Last of Us Remastered.
Other good ones would be Metal Gear Solid 5, The Witcher 3, Fallout 4, Uncharted: The Nathan Drake Collection DriveClub
The Last of Us, Uncharted: The Nathan Drake Collection and DriveClub are exclusives, even though the first 2 are just remastered games from the PS3 but some of the best ones, definitely worth playing if you haven't!
I like Destiny, personally. It's a really good game to kill some time. And you have the option of playing solo or playing with other people (strangers or friends). If someone doesn't like grinding (doing the same thing over and over) they may not like the game though, because there's a hefty amount of that involved.
*Sigh*... Destiny. Eff that game for the time sink it is, but it comes and goes in spurts.
Playing Metal Gear Solid V now, and it's fun but I am a bit OCD about finishing the missions with the best rating and not getting caught, so it's going slow. Painfully slow.
As for receiving a PS4 game for a present, probably Star Wars Battlefront. Not a Star Wars fan, but hey the only game I played for Star Wars was really fun, and I think this takes a lot of influence from it.
All games I guess you could say have a down side for some other people's perspective at least. I don't have many games for the ps4, but I guess you could say in general you can't go wrong with God of War games, The Elder Scrolls games, the Final Fantasy 7 remake still hasn't come out I was really looking forward to it, but now seeing the trailer and reading what the designers of the game have said about the game I am not sure I want to get it anymore because of the vast about of changes they are gonna make in the ps4 remake as opposed to the original that was for the ps1.
My favorite PS4 games are The Last of Us (everyone should play that game, pure masterpiece), it came out for PS3 first, but it got remastered for PS4. The Witcher 3 is also one of my favorites, another masterpiece.
The last of us remastered. It's the best console game on the market. One of the best video game stories I've played in my entire years of gaming. It broke a record recently too... it essentially has won the most awards of any game in history. That alone should tell you something
My favourite game, and pretty much the only one I play, is Football Manager. I play on my laptop, and have played this game since around 1993! It was called Championship Manager up until around 2004. It's a highly addictive football (soccer) management simulation game. New and updated versions come out each year, and for the most part I buy the newer version. Downsides to the game? The game cheats me every time I lose a match!! Haha! :)