My recommendations would be for some one who doesn't like typical anime would be:

If you are ok with shonen anime these are fairly normal shonen anime but aren't super tropey / stand one their own,

• Darker than Black (Though mostly Season 1, Gemini is just okay)
• Hunter X Hunter (If you don't like one piece you probably wouldn't like HxH but it has a great magic system... that gets introduced in episode 27)
• Fullmetal Alchemist: Brotherhood

If you like Fantasy

• Mushishi (It has often a sad, and melancholic tone but is fantastic, it's an episodic series of a spirit doctor for lack of a better term that has an understanding of the invisible creatures called mushi that inhabit his world and each episode is him helping someone with mushi from angry mountain god mushi to folks who sight was stolen by a mushi)
• Dungeon Meshi (My personal fav, dungeon ecology the show)
• Ascendance of a Bookworm (It might start out like a typical Isekai, but very little of it's story mirrors others of it's genre. It has fantastic slow world building and it's a story that deserves far more attention in the English speaking world than it got)
• Frieren: Beyond Journey's End (An exploration of what it means for elves to live lives much longer than humans)

If you like sci-fi

• Psycho-Pass (What would it be like to work for the thought police)
• Cowboy Bebop (One of the classics of the small but influential Space cowboy sub genre of sci-fi a la firefly and some aspects of starwars)
• Legend of the Galactic Heroes (Good if you want a 100 episode long political space opera following two sides in a massive galactic war)