Tokyo Magnitude 8.0 - This is an anime where a brother and sister are visiting a robotics museum when a major earthquake disables all of Japan's public transportation. They have to work together with a woman that they just happened to meet as the earthquake happens to make it home while working with limited food and water and trying to fight off heat stroke. This is a very emotional anime that know how to play your heart like a fiddle.
Chihayafuru - You seem to enjoy a lot of sports anime but here is one that you seem to have missed. It focuses on a game called Karuta which is essentially a game where Japanese poems are written on cards, a reader will start reading a poem and the competitors race to try to touch the associated card first. This might not sound like a sport, but at the top level of Karuta how quickly you can can get your mind and body to react will be the difference between winning and losing. This series not only holds the same level of tension that an intense sports anime does, but it also shows an interesting insight into Japanese culture.
Last Exile - I'm recommending this because I have never really seen anything quite like it. This is a series that takes place in a steampunk world with a few fantasy elements as well. While working on what was supposed to be a routine delivery mission, a pilot and navigator crash land on one of the most feared warships in the world and end up becoming part of its crew. The warship captain takes a liking to them, but they get involved in problems that are way over their heads.
Land of the Lustrous - Here is another recommendation I am making because I haven't seen anything quite like it. This is about a race of rock girls who are fighting off a mysterious group of enemies called Lunarians. It focuses on a girl who really wants to be useful as a fighter, but her body is made of a weaker material then others in her community and they basically think she is completely useless. She will do whatever it takes to prove herself. Even if the premise doesn't interest you I will encourage you to check out at least 1 episode because the art style is really something special.
KonoSuba – God's blessing on this wonderful world! - Probably the funniest anime I have ever watched. This is an isekai where the hero assembles a top tier team of people who have all sorts of problems and they more often win their battles through dumb luck rather than their skills or teamwork.
