There are several westerns I can think of which are classic novels by any standard. I got my book group to read "True Grit" by Charles Portis. ("Masters of Atlantis" by the same author is another underrated work, and sends up secret societies.) There was some resistance to it based on its genre, since the group had not read a western before, but it has a strong female lead character, and some of the members were very impressed by it.

Roald Dahl: "True Grit is the best novel to come my way for a very long time. What book has given me greater pleasure in the last five years? Or in the last twenty? What a writer."

Donna Tartt: "I cannot think of another novel—any novel—which is so delightful to so many disparate age groups and literary tastes [as True Grit]."

The more recent film is more faithful to the novel than the 60s/70s one.

"Butcher's Crossing" is another one that springs to mind.