Izuku missed Kacchan and everyone else that much was a given.
This especially hit him hard when Shinsou Hitoshi, a friend of his from Yuuei, came wandering into the No-Name Town just as Izuku had experienced. Unfortunately, Shinsou hadn't come to the terms that he was dead, thinking that seeing Izuku was some sort of quirk. But Izuku knew that Shinsou would come to realize the truth. While Shinsou mainly shouted at Izuku, he learned that Kacchan was the Number 1 Hero, Shouto was the Number Two Hero and his friends were surviving.
After he had his dinner with Izuku, Ace, and Gintoki, Izuku went back to the Kurosaki Clinic where he spent the majority of his time. If he wasn't teaching, he was helping organize the books that Ichigo and Orihime collected.
Izuku was thankful for the routine. He ate breakfast with the other former OFA holders. He ate lunch at Miss Makoto's shop with Tsuna and any number of people that swarmed the place. He worked throughout the day, helping with Ichigo with teaching, lesson plans and organizing things for the people to do.
Dinner with Asta was the best part of the day. Perhaps it was that they arrived at the same time or that they held the same ideals, or maybe it was just Izuku's ability to be drawn to loud blonds with hearts of gold or that they had easily gotten along which was a good foundation for a good friendship. In truth, it was probably all of these things. Asta was easily Izuku's best friend here. Though no one could replace Kacchan, Ochako, Iida and Shouto in reality, Asta was just so warm and bright.
Which is why when Asta had been unusually quiet at dinner with a pensive look on his face, Izuku knew that Asta must be considering leaving. Izuku had considered leaving to see the rest of the Heroes' Afterlife, but leaving All Might, Tsuna, Nana, Asta, Naruto, Gin, Ace, Miss Makoto, Ichigo and everyone seemed like it'd be too hard since Izuku came to rely on them all. Being dead wasn't easy, but at least, they were all in the same situation.
At the Kurosaki Clinic, he sat outside of the room Shinsou locked himself in. He stared at the door and said, loudly, "Shinsou! It's me again. Just let me know when you're ready to come out and talk."
To his surprise, the door opened. Shinsou, who had grown to look more and more like Aizawa every day (mainly looking exhausted and scruffy), stared down at Izuku. "I'm really dead. And this is the afterlife," Shinsou stated, blankly.
Izuku nodded. He said, "Yeah, I'm sorry, Shinsou."
"Fuck."
"That's generally the mood when you realize you're dead," said Izuku, sympathetically.
"I can't believe I was the second one of our generation to die," complained Shinsou. But then he smirked and said, "But I missed your dumb face, Deku."
Izuku stood up and hugged Shinsou. "I missed you too!"
"Uhhh, affection," said Shinsou, but made no move to get out of the hug. "I guess I should tell you some stuff…"
"That can wait," said Izuku. "The stories aren't going anywhere. We should get you some food. You want ramen?"
"Ramen sounds good."
Once Shinsou was fed and taken to the spare room at Nana's house, Izuku was glad that Shinsou was on the path to handling being dead. Restlessness set in, however, and he decided to take a walk. While it was never night, it was the designated time decided upon to be "night." (It wasn't even a day either. Goku said this place reminded him of something called the Hyperbolic Time Chamber). The town was quiet since it was "night," though Izuku wasn't the only one doing some wandering.
Izuku found himself at the edge of town where he once entered with Asta at least three years ago. To his surprise, he found Asta doing pullups on one of the trees. Izuku laughed and asked, "Are you that bored?"
Asta stopped doing pullups on the branch and jumped down. Asta was happy to see Izuku. He had a big smile on his face. "Izuku! Can't sleep. You?"
"Same," said Izuku.
Without saying, they continued walking back through town. Their easy companionship made Izuku feel comfortable.
"I'm gonna leave," said Asta, suddenly.
Izuku had his suspicions, but to hear it, it made Izuku suddenly very sad. "Yeah?"
"I love it here, but I want to see this afterlife, maybe find a place to start my own farm," said Asta. He shrugged nonchalantly. "Having eternity is pretty crazy."
Izuku nodded in understanding. Being dead meant dead forever. Impulsively, Izuku asked, "Can I come with you?"
Asta looked startled, but then grinned widely. "Heck yeah! It'll be fun. And we can always come back whenever."
Izuku smiled. He didn't know what he wanted to do, but if Asta was going brave the afterlife world, then Izuku should too. Who knew what they'd find out there?