If you're looking for an anime that is not cartoony and more real-life, I would highly recommend "Monster". The art style is realistic, and it is even set in a real world setting (post WWII Germany). The genre is mystery, cat-and-mouse, and psychological. It isn't nonstop action, but it is not boring and it is pretty deep. Best parts about it IMO are the main villain who is rather unique, and the ethical and psychological issues it explores. It also has the benefit that it is a continuous story from start to end.
"Rainbow: Nisha Rokubou no Shichinin" is another possibility, although this is much darker and probably too dark for most people's tastes, so be warned. It's more about survival, brotherhood and honor rather than mystery. Art quality is great though and it is only 26 episodes.
I'd also recommend Ghost in the Shell, which is definitely more mainstream but it's popular for a reason.
Hope that helps