Thanks in advance:
I am looking for good story telling which does not 'rely' on violence, murder, mayhem and rouge, violent, actors to solve the plot. I already have all those names from previous lists. I also don't care for 'romance' novels. Some thrillers are OK if it is more plot and story and less gratuitous violence. Hard Science fiction is good but fantasy is less so for me. I have read all of Ivan Doig, who I found to be a wonderful crafter of stories and characters you can care about. If an author has 15 book on the library shelf, reading one will give you all that author has to offer; the rest will just be variations on the same theme or plot. I read too fast for a book club but I would appreciate their suggestions for material to read. Please give me ideas for going in different directions. I like the challenge and the diversity. All topics are open except the ones I mentioned at the start. I can't afford to purchase new books but I scour the library shelves and order from other libraries.
Again: Thanks for your input!!

Have you tried looking for books on Good Reads? They have really good search criteria for finding subjects and similar authors.

Rosamunde Pilcher paints an alluring painting of Scotland that is not soon forgotten.

Have you read the 40+ James Michener books. Enjoyable reads with a mix of fact and fiction, generally taking place in a location over multigenerations.

James Doss and his books about the Ute Indians. They are mysteries (somewhat) and also about the indians. My husband has read all of them to me at least twice each and we really enjoy Doss's sense of humor.

Unfortunately, Doss went and died. We really miss any new books of his.

Tony Hillerman is another fine author. He writes about the Navajo down in New Mexico. Not only does he develop his characters well, he uses real places in NM and it's fun to recognize the various towns and places where my husband and I have traveled.

Right now, my husband is reading "Why Beauty Is Truth: A History of Symmetry" by Ian Stewart to me for the second time, I enjoyed the book so much. This is a fascinating history of mathematics and symmetry. You don't have to love math to really appreciate this book. Stewart starts way back with the "Scribes of Babylon" many thousands of years ago and how mathematical thinking started and travels through the evolving concepts of symmetry.

What's also very interesting is Stewart gives personal histories of some of the great mathematicians. They have somewhat crazy lives that show mathematical brilliance doesn't always transfer to living a life. For example. one of the great French mathematicians (Galois) died at a young age in a duel.

I think that Jodi Picoult could do the trick. I also like Jacqueline Mitchard and some of Anita Shreeve's books.

Kent Haruf...a Colorado author who writes quiet, spare, satisfying novels about life in the fictional Eastern Plains town of Holt, CO. "Plainsong" has always been my favorite. Great characters!
Prior to his passing in 2014 he also published: "Where You Once Belonged", "The Tie That Binds", "Eventide", "Benediction" and "Our Souls at Night".
I can't recommend his work highly enough. He is missed.

Other obscure (to me, anyway) novels I have read & were enjoyable surprises:
"March" by Geraldine Brooks. Learn what the absent father of "Little Women" was experiencing in the Civil War. Also, by the same author, "Year of Wonders", a fictional account of a self-quarantined village during the days of the plague in 17th century England.
Another thread pulled from an American classic is "Finn" by Jon Clinch. Learn about Huck's father. Very dark, but interesting. Mr Clinch was very respectful of taking an idea from Mark Twain's iconic story and running with it.
An afterthought - Mr Finn is depicted as a damaged SOB. This book may meet the standards established in your OP. I'm making an assumption you are dismissing only gratuitous violence. "Finn" is not that, but is hauntingly dark.

Local/Conifer author. A Chick in the Cockpit by Erika Armstrong. Comes with a list of discussion questions.
https://www.amazon.com/Chick-Cockpit-My-Life-Air/dp/1933016140/ref=sr_1_1?ie=UTF8&qid=1481135732&sr=8-1&keywords=a+chick+in+the+cockpit

If you like Ivan Doig, try Mark Spragg. He wrote Fruit of Stone and An Unfinished Life among others. These are fiction and really good stories. Also he wrote a memoir/autobio called Where Rivers Change Direction.

I love all the suggestions!

I just started a book by James Carlos Blake but it might contain more violence than you stated in your OP. I have family in the Brownsville, TX area and these few books about the Wolfe Family are based loosely on his own family from that area and Mexico.

He writes other historical fiction and historical non-fiction but it seems to be based mostly in the Rio Grande Valley area of deep south Texas. Just a thought.

I'm going to look into the other suggestions here - what a great topic!