john ford is widely considered a master and he directed a bunch of john wayne movies. THE MAN WHO SHOT LIBERTY VALENCE is probably the best of them that i've seen, but STAGECOACH and THE SEARCHERS are also good if you can get past the ultra dated comedy in places. also heard good things about THE QUIET MAN, THE LONG VOYAGE HOME, SHE WORE A YELLOW RIBBON, FORT APACHE, all directed by ford and starring wayne.
RIO BRAVO is pretty great too, directed by howard hawks who was a huge influence on guys like john carpenter, michael mann, tarantino, scorsese etc. he also did RED RIVER, EL DORADO and HATARI! with wayne, all on my wishlist.
he was also in a movie directed by DIRTY HARRY's don siegel, called THE SHOOTIST, which also stars jimmy stewart, lauren bacall, ron howard, john carradine and scatman crothers, which sounds insane.
i think wayne was more of an iconic presence and embodiment of american values than a guy with good acting range, which explains why it seems to have taken great directors to put him in the right context and get the best out of him. supposedly he mostly just played himself.