[Jiggly]

Depends on your tastes. What kind of anime are you looking for?

He's sort of indicated what stuff he's enjoyed before, and said he was looking for a few mecha shows. Perhaps you could recommend one or two mecha shows?

[Skullmeat]

Muv Luv Alternative: Total Eclipse
https://myanimelist.net/anime/11021/Muv-...al_Eclipse

Aldnoah.Zero
https://myanimelist.net/anime/22729/AldnoahZero

Mobile Suit Gundam 0083: Stardust Memory
https://myanimelist.net/anime/84/Mobile_...ust_Memory

While its a bit more mainstream than others I've listed here, Stardust memory is too good not to include.

[Oni]

If you enjoy pre-2000 anime, you might like Bubblegum Crisis or A.D. Police Files. Not for everyone, though.

[claire124]

Fruit basket, I don't think someone has heard about this anime.

[lionelvidal]

Tatami galaxy ( story about a NEET that struggle to find friends)

[apostoins]

Try Jujutsu Kaisen, you will like it a lot

[ColeSmith]

I'v seen a few hundred anime, and was just wondering if anyone can recommend any anime that is good, non-mainstream, and something that I probably never watched before....

I can recommend you berserk 1997. You might also like One Punch Man. These are masterpieces!

[GraceFmJKing]

Try to watch Grand Blue, it is a great anime comedy

[SnigMonis]

Vinland Saga is not so popular but amazing

[waseem2341]

May be u should try this
Fumestsu no Anata e (2021)
Rainbow
Mushishi
Eden Of The East
Spice and Wolf
Wolf children (movie)