I would suggest you check out Luther, Survivors, Breaking Bad, and Archer. The first two are British shows. There is violence in both of them, but it isn't the defining characteristic of either show.

Luther - This is the story about a cop in Britain (Idris Elba, Stringer Bell from the wire) trying to fix his broken career and marriage. He deals with violent offenders and gets too caught up in his work. I don't want to give away too much of it, but most people are hooked by the first episode. Elba won a golden globe for his performance.

Survivors - This one is a short series that takes place in the UK right after an epidemic wipes out 95% of the worlds population. It is your typical post apocalyptic initial plot, but the acting and the writing is top notch. It is a little slower than Luther, but certainly worth the watch. The pacing is a little quick because the season isn't 26 episodes.

Breaking Bad - This one was previously described above.

Archer - This is an animated series geared towards adults. It airs on basic cable so the nudity level is kept PG, however, the jokes are not. The story follows Sterling Archer. He is spy for Isis and possibly the best or worst spy ever. He's very good at getting things done, but he's terrible at keeping secrets because he uses the fact that he is a spy to pick up women and to brag to anyone who will listen.

All of my suggestions can easily be found on Netflix watch instantly. I would start with Luther and Archer.