One common theme is adventure. The reader often goes on exciting quests or missions with Azriel. For example, they might explore a mysterious new land in Prythian together.
There is a popular 'azriel x reader fanfiction' titled 'In Azriel's Arms'. It's a must - read because it shows a very unique side of the relationship. It has a great plot that keeps you hooked from the start, with the reader character having some really interesting interactions with Azriel.
You can try looking on Archive of Our Own (AO3). It has a large collection of fanfics, and there are likely many azriel x reader ones there. Just use the search function and type in 'azriel x reader' to filter the results.
Tumblr can be a good source too. There are many blogs dedicated to fanfiction, and you might be able to find some amazing 'azriel x reader fanfiction' by searching relevant tags or following the right blogs.
One common theme is adventure. Since Eureka Seven AO is set in a rather adventurous world, the fanfics often involve the reader going on exciting adventures with AO. Another theme is friendship and loyalty, as they face challenges together and rely on each other.
Love and longing are very common. Since their relationship in the original context has a certain allure, fanfictions often explore the deep, unspoken feelings they might have for each other.
One great Eureka Seven AO x reader fanfic is 'AO's New Adventure'. It really delves into the relationship between AO and the reader in a unique way. The author does a wonderful job of bringing the world of Eureka Seven AO to life and making the reader feel like they are truly part of the story.
One great 'elain x azriel fanfiction' is 'The Unseen Bond'. It beautifully explores their relationship with a lot of emotional depth. The author really captures the essence of their characters.
You can try searching on popular fanfiction websites like Archive of Our Own (AO3). There are often a large number of fanfics for various pairings, and it's likely you'll find some great 'elain x azriel' ones there.