One possible scenario in a Naruto and Riza Hawkeye fanfiction could be a dimension - hopping adventure. Naruto, with his boundless energy and ninja skills, could end up in the world of Fullmetal Alchemist where Riza Hawkeye resides. Riza, being the skilled sharpshooter she is, might initially be suspicious of Naruto. But as they face common enemies, perhaps some alchemist - turned - villains who are after a powerful chakra - based artifact, they start to work together. Naruto's Rasengan and Riza's precise shooting could make for some amazing battle scenes.
A fanfiction could also focus on a training arc. Naruto could train Riza in chakra control, which she could then use to enhance her shooting accuracy even further. In return, Riza could train Naruto in marksmanship, which could be a useful skill for him in certain situations. This could lead to a friendly competition between them, with both of them constantly trying to outdo each other in their respective skills while also growing as individuals and friends.
One interesting 'naruto hawkeye fanfiction' could be about Hawkeye somehow getting transported to the Naruto universe. He might use his archery skills in a unique way, like against the ninja's jutsu. Maybe he teams up with Naruto and they learn from each other's combat styles.
Another way is to join Naruto or Hawkeye fan communities on social media platforms like Reddit or Discord. Ask the members there if they know of any good 'naruto hawkeye fanfiction'. They might be able to recommend some great stories based on their own reading experiences. Also, some of these communities might even have their own collections or lists of recommended fanfictions.
On the other hand, if some of the fanfiction was a bit too outlandish or inappropriate, it could make things a bit awkward. Hawkeye might feel embarrassed, and the other Avengers might not know how to react. But they'd probably try to smooth things over and remind Hawkeye that it's just the creativity of the fans and not a true representation. They'd still support him as a teammate.
Hawkeye fanfiction often emphasizes his skills as an archer. For example, stories might focus on his amazing accuracy and how he uses his arrows in creative ways. Also, his relationship with other Avengers can be a big part of it. He's sometimes shown as the underdog among the super - powered heroes, so stories may explore his insecurities and how he overcomes them. Another characteristic is that it can take Hawkeye to different settings, like a noir - style city or a fantasy realm, which gives a fresh perspective on his character.
Another possibility is that Hawkeye is on a mission in a world where magic exists on the fringes. He meets Hermione, who is researching ancient magical artifacts that could have an impact on the Muggle world. They start off distrustful of each other but as they learn more about their respective worlds, they form a bond and work together to protect both worlds from a common enemy.
Tony Stark would likely find it hilarious. He'd probably be the first one to start making jokes about it. He might say 'Oh, Hawkeye, you've got some really creative fans out there. I should hire them to write my memoirs!'. As for Hulk, he probably wouldn't care much. He might just grunt and go about his business. But if he did read some, he might not understand it very well and get frustrated. Hawkeye himself would probably be embarrassed at first, but then he'd start to see the humor in it and might even enjoy some of the more positive fanfiction about him.
Archive of Our Own (AO3) is a great place to start. It has a large collection of Hawkeye x Reader fanfictions with various themes and styles. You can easily search for what you're interested in using their search function.
One great Hawkeye x Reader fanfiction is 'A New Beginning'. It beautifully captures the relationship between Hawkeye and the reader character. The author does an amazing job of showing how the two meet and slowly develop feelings for each other.