I remembered earlier how Nolan North (plays David) let slip there will be a new TLoU. And also how Troy Baker (plays Joel) knows nothing.

This could suggest that there's no Joel in the next game... but that's just a possibility still at this stage.

Anyway, what would you like the next instalment to be about?

Focus on a character from TloU, show how they got to where they are (e.g. David, Joel's brother, Tess etc)

Have chapters on a few different characters with their own separate stories

The early years of Joel (and Ellie), how he survived the fall and got to where he did.

A direct following sequel to TLoU, I think the first game does leave this possibility.

Completely New characters, set in a different part of the states, or world even. 

Or something else! I know a user on here wants an open world online game set in the universe.

That's Left Behind lol

Brand new characters with own story. Last chapter they meet Joel and Ellie in the period after TLOU.

EDIT:
TLOU 3 - 4 player coop

TLOU 4 - Joel's prequel story. The End.

Maybe what happens between Joel and Tommy. So like what happened between the end of the first section of the game until you start playing as Joel again with Tess.

Something on the lines of Metal Gear Solid 2 would be awesome. A contemporaneous deconstruction of society, but unlike the media saturation and manipulation as the main point (like MGS2), the ethics and morals of a post-apocaliptic survivor/society.

I'd also be cool with a protagonist swap if it serves to see how much the original cast progressed through the years.

I'd be interested in seeing Joel in the years after his daughter's death. Tess was a great character and it would be nice to see more of her. How she met up with Joel, how they came to trust each other, the hardships they had to face.

I want a sequel with a tribe of immune descendants of ellie dealing with infected with increased intelligence and the moral implications of who actually should rule the world and a possible sybmiotic relationship, while both being wiped out by the last human survivors in the end.

Someone should play the Metro games, if he hasn't already, of course.

I'd like to see a whole new cast of characters and a new story in the same setting. Maybe they could meet Ellie, or someone from the first last of us down the line, but it shouln't be the focus.

I want it to have a hidden ending Farcry 4 style. You start out in the hospital at the end of the last game and have to make the decision again. When you let them kill Ellie, the game is over and you will see what a disease-less paradise the world will become. Or you choose the regular end and have to play the game in a dystopian hellscape.