In my opinion, asking for movies to be good Conan stories, I think atmosphere and feeling is paramount. If so, we must remember that Conan is adventure pulp, since Howard loved to write such, creating a fantasy world out of the hints of others. Howard enjoyed much more writing tales like Three-bladed Doom. But everything that was written in pulps in the pulp era, no matter the setting, had the feel in common. The best inspiration then would be films completely based on those pulp stories, that really capture the feel.
That is, the Indiana Jones films, and the already mentioned Mummy films -specially the 30's version- and obviously King Kong. Almost much better than Gladiator, which is a quite different kind of story. Big Trouble in Little China would do fine if you strip all the modern touchs. And there are many more films, but I'm just giving a guideline here.