Most of my exposure with anime was whatever was on Toonami and Adult Swim in the 2000s. I've not watched stuff like, Ghost In The Shell, Cowboy Bebop (only disjointed episodes out of order), Neon Genesis Evangelion, which I know are highly regarded.
I've seen just about every Miyazaki movie at this point. I've seen Akeria.
I'm sure there's more mainstream shows and non mainstream shows that I'm missing and would enjoy.
Thoughts?
Notable ones from recent years:
Birdie Wing - Lesbian golf anime. A European girl competes in unsanctioned underground golf tournaments to keep her family afloat, falls into love/rivalry with Japanese (underground unsanctioned) golf prodigy. Don't worry if you have no interest in golf whatsoever, this anime makes golf look like an actually interesting sport
Mob Psycho 100 - Wholesome, wacky, subversive. A shy, physically unfit, unpopular at school just so happens to be born with psychic powers greater than any other living human. However, the focus is the journey he has in improving himself physically, becoming more socially outgoing, and emotionally stable. He genuinely wants to live life where he succeeds or fails based on his effort rather than using powers given to him at birth. 3 seasons, fully contained story.