I was fortunate enough to buy The Last of Us Game of the Year Edition that also had the DLC. I did not have high expectations of the DLC, but since I loved the main game I said to myself to also play the DLC. I will try to keep it as spoiler free as possible.
I think the DLC is placed before Ellie's encounter with Joel. It is a nice in-depth story about how Ellie survived on herself, despite being a child. It also give the players and idea about Ellie's personal life. I find the DLC to be the perfect companion to the main game and it is a must play if you want to understand Ellie and the story of the game. The DLC is not as long as the main game, but its story is very well told. The DLC is not artificially extended and it has the right amount of gameplay after hours put into the main game.
I also love the fact that The Last of Us 2 ties in with this DLC (this is also the reason why games are to be played in order: main first game, DLC for the first game and then the second game).