Mature Anime?

Hi! I'm an avid anime watcher (possibly otaku) here and I might be able to suggest something.

I'm sorry to say I have never watched Welcome to the NHK, though I think I have an idea of what you are looking for.

I suggest anime tagged Seinen/Josei which are targeted to an older audience than shounen/shoujo.
Personally, I recommend Princess Jellyfish (which is Josei, btw) an anime also about otaku people dealing with the world as a new character steps in and changes their life. Its an anime that my telenovela buddy who is as far as you could get from otaku, watched and fully enjoyed, so please give it a try if you haven't already!
If you are still skeptical, there is a Japanese movie of Princess Jellyfish out as well~

I watched Michiko to Hatchin there's a while but it was good yes!
Space brothers maybe?I m reading it in manga and it's good , the adaptation seems fine too ( uchuu kyoudai) or Planetes?

NHK ni youkoso is a fantastic anime 

chihayafuru - it's josei. the artstyle characters and feels are to the max

I liked Welcome to NHK but I don't believe there is anything even remotely similar to it. In general if you want realistic you have to look towards older anime, for example before 2010.

Cowboy Bebop can be considered mature. Fantasies can be mature as long as they have realistic themes.

There is a famous director that makes realistic anime movies, Makoto Shinkai, his most popular/successful movie is not so realistic but still good, you probably heard of it - Your Name, I think 5 cm/s was the most realistic, and depressingly so.

Otherwise, I also found these realistic:

Fullmetal Alchemist (2003 ver.)

Rurouni Kenshin Tsuiokuhen - flawless anime, helps that it's short

Samurai Champloo

Mushishi

Some Gundam stuff give realistic depiction of war: 08th ms team, Gundam 00

Sports: Major, Slam Dunk - nothing like Kuroko no Basket or Prince of Tennis

Hope that helps, I'm a big advocate of realism in fiction.

You can read/watch Josei manga/anime. Watashitachi wa douka shiteiru is good. There isn't an anime, but there's a live action drama. An Incurable case of love/love will last forever has a Live action too. if you're in to romance.

 plottwist:

I'm looking for anime, like Welcome to the NHK, that are little bit more grown up and serious about topics. I like all genres except school life. thanks

idk about much Josei anime, because most Josei manga don't have anime adaptions.

But if you like manga you can read: watashitachi wa douka shiteiru 

there's a live action too