I agree with silenus about Red River.
I agree with the two lists that were provided you, but I think I would add McClintock to the westerns. He and Maureen O’Hara worked so well together. Some of the featured players (like his son and for that matter Jerry Van Dyke) were very weak, but it is great fun none the less.
I also would add to the list of non-westerns, Blood Alley. John Wayne is riverboat captain in China. It also stars Betty Bacall. There was a weird sort of chemistry and worked in a strange sort way. It was one of his few anti-communist related films that worked on any level.
It’s not one of his best but it is fun nonetheless, War Wagon, a kind of western heist film with Kirk Douglas, Howard Keel and Kynan Wynn.
I can almost recommend Big Jake. The scenes with O’Hara are very good and the ones with Richard Boone are wonderful. His scenes with the dog are even very good. But when you bring his son in, Robert Mitchum’s son in and Bobby Vinton in it was painful.
Another fun (but flawed) one with not a lot of substance was a sort of Western. I guess you could call it a Northern. “North to Alaska” with Stewart Granger, Ernie Kovaks and Fabian. Not much there but the fights were good.
Wayne was never afraid to bring in good actors to star with him. But he was also not afraid to bring in people who had no idea of what they were doing. He always figured that he and Ben Johnson could carry it if necessary. When he didn’t have people like his son Patrick, Bobby Vinton, or Fabian screwing everything up he had some great films. Actually he won his academy award when Glen Campbell was cluttering up True Grit, so I guess he was right to a certain extent. I always blamed it on Ricky Nelson who did a good job in Rio Bravo and thus letting Wayne think that young singers could act.
You should also get The Conquerer just so you don’t think that Wayne couldn’t make a bad film. It wasn’t all his fault, but he took part. That’s the one where he played Genghis Kahn.
*FWIW - I appeared in four films with John Wayne later in his career. No, I am not a big-time actor. I was a "type’ who could sit a horse, drive a wagon, held a SAG card and lived not far from where a number of his Westerns were made. He was a nice man. While most of the “name” actors would have nothing to do with us or the extras, he would often sit and visit with us, buy us beers and remember our names. *