Best story... Witcher 3 hands down. Thats the new benchmark IMO.
Other favorites.. The Borderlands games. 1, 2 and the pre-sequel tied in pretty nicely, the pre-sequel didn't have the sparkle that the fiorst or second did as far as me wanting to do a second playthrough, but it didn't leave a whole lot of holes. Whomever the bad guy is in Borderlands 3 has some serious shoes to fill to replace Handsome Jack. That guy was a son of a bitch, but the kind of son of a bitch that made you like him. Anybody that can buy their own pony made of diamonds that poops cool guns can't really be all bad.
Dying Light and the Following DLC has a really good story and friggin AWESOME gameplay. Its DEFINITELY worth 2-3 play throughs because of all the cool weapon mods, the buggies in the following, and despite it being almost 3 years old, the graphics are still amazing.
I liked all 3 bioshock games, but it was stated earlier, they were a once and done. Pretty games, killer story, but they didn't get a 2nd play through.
Dead Island and Dead Island:Riptide were excellent games too, but there were a bunch in our Steam group that got both games when they first came out and played each of the 4 characters and leveled them to their cap. They're good games to co-op, single player is kinda meh.