I'd warn you to be aware that there is so much variety that one person's top 10 list will be another person's "don't ever waste your time" list. I would also warn you that many of the "great" works from the last century did not age well.
I'm not saying this to take away from those works, but to let you know that as you dig in, if you find a few that you really dislike... just put them aside and try another. You'll find the authors and styles you enjoy.
Second the recommendation for the Bobiverse series; it's a fun series and I'm looking forward to the 5th book.
Also Andy Weir's Project Hail Mary is an excellent read!
A tiny random trilogy of books worth reading for various reasons:
Ursula K. Le Guin: The Left Hand of Darkness
Arthur C. Clarke: Rendezvous with Rama
Robert L. Forward: Dragon's Egg
There's quite a breadth and depth to the genre, I'd suggest not spoiling things by reading book reviews, but you might enjoy reading about the three authors above.
and then there's Philip K. Dick (and many many others).
Note for OP: While a big theme in the book is how Earth evolves between war deployments, much of the Forever War takes places elsewhere in the universe
I'm surprised no one has mentioned Adrian Tchaikovsky yet. I rather enjoyed the Children of Time and The Final Architecture series. They both technically contain bits of Earth but should still fit into the conditions you're after.
I'm curious what it was about Final Architecture that made you not continue. As I found myself hooked. Just looking to hear an alternate perspective is all.
I have a hard time getting into non-hard-scifi / space-operas. It felt like the rules were loose. Good read, but didn't move me the way Children of Time and sequels did. Ie, Children of Time felt like something Stephenson or Andy Weir would write; Shards of Earth felt more... I don't know. Almost satire?
Ringworld by Larry Niven. Technically you should start with Neutron Star by the same author, but if you're not familiar with the Known Space universe, I don't think it's a big deal to start with Ringworld.
One of the few Sci Fi novels to win both the Hugo and Nebula awards in the same year!
Is it cheating to recommend Anathem, regarding not set on earth? It's an outstanding novel, set on an earth-like world.
If you want something more out-there, Verner Vinge's A fire upon the deep and its sequel are great. Or, as recommended by another poster, The Children of Time trilogy.
Although Earth is part of the story, it isn't at all the focus and there are other settings, and it is 100% absolutely worth a read: The Expanse series. 10 books. Brilliant prose, brilliant sci-fi. Incredible audiobook narration if that's your thing.
Hyperion by Dan Simmons
The forever war by Joe Haldeman ( some of it is on earth but it’s mostly off world)
Solaris By Stanislaw lem
It’s been a while since I’ve read The Left Hand of Darkness by Ursula K. Le Guin, but I think it’s off world too.
Foundation series is my favorite. Read the Robot and then the Empire series by Asimov which are all set in the same universe as Foundation. Not as good, but there will be some pleasant surprises.
Dune and sequels by Frank Herbert are the next logical option, with similarly large scope.
The Expanse series by James S.A. Corey is great, set in the solar system in the near future.
Andy Weir's Project Hail Mary and The Martian are super fun reads, technically fulfilling the "not on Earth" requirement. Both are about one person's overcoming great odds, so a very different brand of sci-fi.
Culture series by Iain M. Banks. There are 10 books. It's about a utopian galactic civilization governed by super AIs. Most of the super AIs are giant spaceships that transport people. Most people live for 500+ years, and a lot of them switch sexes. People also have drug glands which allow them to instantly administer 200 different drugs via mental trigger.
Marrow - A group of people find a Jupiter sized ship of unknown origin and start a galactic cruise with many different species in the far high tech future.
The Stars My Destination
Starship Troopers - very different from the movie, sci-fi classic. Even on the Marines reading list.
Forever War - partially on Earth most in far flung space battles.
The Martian - solid Jew hard sci-fi again very different from the movie
Plenty more but, sadly sci-fi falls under Sturgeon's law.
The lesser known but inspiration for some well known authors [1]: [Jack Vance](https://en.wikipedia.org/wiki/Jack_Vance).
I can highly recommend "The Demon Princes", "The Cadwal Chronicles" and "Tschai".
I recommend diving into "The Left Hand of Darkness" by Ursula K. Le Guin, "Dune" by Frank Herbert, and "Hyperion" by Dan Simmons. These novels offer richly imagined worlds beyond Earth, exploring captivating science fiction landscapes and narratives.
Citizen of the Galaxy - despite being one of Heinlein’s “juveniles” is an interesting and entertaining exploration of the balance between freedom and duty.
I’m a big fan of Lois McMaster Bujold’s Vorkosigan series. It’s not hard sci-fi. Earth is in the stories, but not the central location for hardly any of them.
I recommend reading them in chronological order, rather than published order.
I'm not saying this to take away from those works, but to let you know that as you dig in, if you find a few that you really dislike... just put them aside and try another. You'll find the authors and styles you enjoy.