Kyoukai no Kanata: Akihito is a half demon, though he looks human. His heritage makes him immortal. One day in school (the setting seems to be modern day) he meets Mirai, the descendant of a clan of excorsists, who can make weapons from her blood. Their friendship (if you can call it that: she stalks Akihito to attempt to kill him every day) starts off shaky, but then he decides to help her.
We liked this one. The setting seems modern day but with demons added, which makes it both relatable and weird enough to provide adventure. Animation quality is good, and I liked the character designs. The subtle mannerisms of the characters provide good clues as to their personality, which is something that you don't see too often.
Coppelion: A disaster turned Tokyo into an irradiated wasteland. Three girls, clad in school uniforms, walk into the capital in search of people to rescue. They can survive the asphalt jungle because of their engineered genes, where other people have to rely on protective suits. Their search leads them deep into the city.
OK, so there's been a disaster a few years ago. How is it possible that there are still people in Tokyo that need to be rescued after all that time? Either they've evacuated or they're dead, right? The logic behind that isn't explained in the first episode. But we liked it a lot: the premise is interesting, and the characters are likable. The backgrounds are gorgeous, and it's fun to see what a city in ruins might look like.