The Disappearance of Nagato Yuki-chan was originally a spin-off manga to the light novel series Haruhi Suzumiya. Adapted into a 16 episode anime (plus an OVA that was released with the manga's ninth volume), it takes place in the alternate reality that was shown in the movie The Disappearance of Haruhi Suzumiya. In this alternate world, Nagato is not an alien, Mizuru is not a time traveler and Koizumi is not as esper. Rather, while Nagato is still the president of the literature club, she is shy and quiet, and would prefer to be lost in the gaming.
The anime starts off with Kyon already joining the literature club and we get an idea of the tone of the series. It shifts to a much more lighthearted and comedic tone filled with gags, chibi art shifts and highly exaggerated motions. Asakura is Nagato's best friend and fiercely protective of her. She tries her upmost best to pair Nagato and Kyon together, of which there are obvious, reciprocal, feelings.
The main characters from Haruhi Suzumiya show up in their own way, including Haruhi herself. There are a few episodes without her and it feels fine. When Haruhi does turn up, it feels like that she is starting to take the attention away from Nagato instead and that's a shame. Haruhi ends up becoming a bigger plot point. Her personality and interest in the unknown remains the same but just that she doesn't actually have the power now to rewrite the world. The best thing is that all the side characters that were kind of brushed off before now have bigger roles.
The change in art style compared to The Melancholy of Haruhi Suzumiya takes some getting used to. This spin-off is best watched after you have finished the first two seasons and the movie as you would be able to pick up on a lot more references this way. Seeing the references, and knowing what the characters are alluding to is a lot of fun and a huge part in the enjoyment of this spin-off. The anime is part of the slice-of-life genre as the characters get into their usual antics, and then have to find ways to resolve it. It mostly revolves around Nagato's crush towards Kyon and the many ways she is trying in order to reveal it to Kyon. Beginning with Christmas, the club members tries to organize a Christmas party. It is also at this time that Nagato has to try to recruit more members in order to keep the club open.
Once all the characters joints, it gets livelier and you half expect things to return to the way it was when they were the SOS Brigade. You have to get over the fact that this Nagato is more expressive and shows her emotions much more plainly compared to her alien counterpart. Asakura, and eventually Suzumiya, are the main catalysts for everything that happens in the series. While everyone's personalities are somewhat recognizable, they each have new elements to them. It's hard to get over the fact that Nagato changed so much and now loves food as well. In a way, it is super similar to The Melancholy since it revolves a lot around the club's activities, but feels more generic.
The club ends up doing activities such as a trip to the hot springs. Kyon and Nagato have a lunch together as they (subconsciously) flirt. It all feels like something you have seen before and does not surprise you at all. That isn't to say that it doesn't have its charming parts. The characters still carry enough charisma to be fun. In an interesting turn of things, the middle of the series departs from what you'd come to expect up until that point. It is a lot more serious as Nagato's personality changes for better or worse. If you have been enjoying the calming and lighthearted atmosphere up until that point, then these episodes are a hiccup and doesn't quite gel with everything else. It is also from this point onwards that you feel that there is a stronger connection to The Melancholy. You can see the parallels in plot lines, as well as this version of Haruhi sharing a similar past.
That being said, the second half of the series pushes forward the main arc, that of Kyon and Nagato's relationship. There's a bit of tension as well as awkwardness, and it becomes the sweeter when you see how the pair end up resolving those issues. The OVA starts off by bringing back (potentially bad) memories of the Endless Eight loop of episodes. Thankfully, it puts on a better, more lighthearted spin on it and ends up being very enjoyable and funny.
Overall, if you go into The Disappearance of Nagato Yuki-chan without expecting that it'll be similar to The Melancholy of Haruhi Suzumiya then you'll be fine. It is a more lighthearted and funny series that works really well as it explores how the cast spends their time now that Haruhi isn't the driving force. While the sudden change in Nagato's personality and consequential shift in tone felt like it clashed with the rest of the episodes, the series is a lot of fun.
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