I enjoy all of them in their own seperate games, like lasting appeal and extreme re-playability of Binding of Isaac: Afterbirth, story and gameplay of Dark Souls 3 and Xenoblade Chronicles, OST of all of them and such...
Lasting appeal as well as it's ability to be difficult enough to keep you on your toes, but not impossible to the point of restricting you to only using certain methods to beat.
I'm honestly glad to see no one has voted for graphics yet. Why do you need 4K? Why do you need 1080p 60fps (granted that's standard but still)? It's a game's overall appeal that matters. Take Ocarina of Time for example. A lasting legend (hehehe) in the series. It's only 64 bits (if you don't count the 3DS remake) and it's not very aesthetically appealing compared to today's standards. But it's overall appeal is just up the charts. Why do you think it was voted 1998-1999 GOTY? Graphics may be preferred high quality, but play EathBound or Super Mario World on the original SNES and tell me they're not good with a straight face looking me in the eye.
I usually look at the multiplayer or how gameplay is. But mostly gameplay. I concentrate on seeing how the mechanics in the games works and how complicated it is to handle said mechanics. I also concentrate a lot on button handling and limitation on buttons. You don't know how much I get disappointed when I get a game where gameplay does not allow you to run and move the camera at the same time.
Voted for the Story/Campaign Mode since it's what gets me hooked into the game itself, but furthermore I value, Replayability. It's just that some games just goes down in your storage/stall/shelf/wherever after playing them, while some gets stucked on your mind that you can even play it again and again without having a diminished satisfaction of playing the game. For example, I believe most of the gamer population out there would definitely agree that having a Final Fantasy rework would be really nice since it's one of the top games with high replayability value.