It depends on what you liked about those books.

If you want more Ishiguro, then maybe try his first book A Pale View of Hills so you can see how he started, or Klara and the Sun, his most recent book which was well received. I haven’t read it though but I plan too. 

Some other works are more experimental / surreal though like The Unconsoled and Buried Giant, so they are polarizing, but I like that kind of writing too.  If you decide to read Unconsoled, try reading/listening to Ishiguro’s short story first, which I linked in this comment here.  Be sure to listen to the post-story discussion as it’ll help you prepare to read The Unconsoled.

What I particularly like about Ishiguro is his exploration of narration in fiction (how the story is told to you by a narrator, in Isiguro’s case, it’s usually a 1st-person narrator), and that the"truth" that they see is just a kind of story that can be easily altered by memory and by one own subjectivity (how they interpret those events). These narrators often have a kind of flaw. 

Try Blind Assassin or Oryx and Crake by Margaret Atwood with are both fantastic books. Atwood often plays with narration and uses language in interesting ways. Both books involve an attempt at organizing the past, similar to Never Let Me Go and The Remains of the Day. 

In Oryx and Crake, Atwood mixes both present-tense first-person narration with omniscient third-person narration. It portrays a man in a post-apocalyptic future trying to tell himself a story about his own past. When inside his mind, the narration shifts to him as a storyteller and it switches to third-person narration. There are also people within his narration that tell their own story of the past occasionally, so the book has many layers. 

Blind Assassin is a great mix of different genres: gothic mystery, romance, adventure and a touch of sci-fi. The book deals with narration and storytelling as well. Atwood likes to play with language in more overt ways than Ishiguro but she’s just as powerful.  Maybe try this book first. 

The Cat’s Table by Michael Ondaatje is similar to The Remains of the Day because it also has a flawed narrator. It’s about a boy setting sail from Sri Lanka to England, and the story shifts between the ship and his adult years. I haven’t read this yet, but it’s been on my to-read list for a long time, and it’s often suggested as similar to Ishiguro’s books. 

Sense of an Ending by Julian Barnes is also good as well, and also has a narrator trying to make sense of the past through his recollections.  It’s a short read, almost like a novella rather than a novel.   

“A Bullet in the Head” by Tobias Wolff is one of my favorite short stories ever. It’s about a man recounting his entire life in a split second.  This story hits you hard.  You can find it in his short story collection The Night In Question: Stories but it’s also been included in many “best of” anthologies.   

 “Death by Landscape” by Margaret Atwood – I know I’ve mentioned her often, but this is another story that absolutely blew me away. It also deals with recollections, about how this one painting conjures up all these memories for the narrator, in a very haunting and evocative way. It starts slow but like The Remains of the Day, it gradually builds up the tension.   You can find the story in many anthologies as well, and also in her Wilderness Tips collection. 

For something more conventional, try: 

Of Human Bondage by William Somerset Maugham

Like Water Like Elephants by Sara Gruen

I was really moved by both novels. Gruen’s book alternates between the past and present, and you learn a lot about Depression-era America. It’s an interesting combination of history, adventure and light romance. 

Maugham’s book is really old but it still resonated with me: a story of a young man’s life in the early late 1800s / early 1900s, a rare peak at what life was truly like in those times in the US and Europe.