I could never really get into Steins;Gate, mostly because pretty much every time the MC opened his mouth, I wanted to punch him.
I’d say that the greatest sci-fi anime, mecha or not, is Cowboy Bebop. A pretty mundane answer, but it just is what it is.
My personal favorite is probably Kaiba. I’m also especially partial to Trigun (including Stampede), Ergo Proxy and Yokohama Kaidashi Kikou. And I feel like I shouldn’t let this go without mentioning Now and Then, Here and There, Casshern Sins, Darker Than Black and Aria. And a couple of cheesy gems that aren’t even close to the greatest that I just happen to like - Estab-Life and Photon: The Idiot Adventures.
The Legend of the Galactic Heros
Edit: +Die Neue These
I’d consider “A Certain Scientific Railgun” sci-fi-ish; it was my first real entry into anime and is still one of my favorite anime ever.
Shin Sekai Yori. I don’t think I can say literally anything about this without spoiling it; it’s one that is so much better if you go in blind.
Fantastic show took me a while to convince my friends to watch it while not describing it at all
I want a slice-of-life-in-space. No slap-stick, no comic relief, no meta jokes that reference current events as “ancient”… i just want to watch people living in the future.
Here’s a 6 year old reddit post with suggestions
I’ve only watched Planetes and Outlaw Star from the list, but I think Planetes comes closer to your taste.
Serial Experiment Lain
Legend of the Galactic Heroes