A few nights ago I was reading Hershel Shanks’ case (not online) for David’s tomb being the rock-hewn shafts excavated by Raymond Weill. I think he’s wrong, but I think he has presented the best case that can be made. And he can’t be far off geographically.
The traditional tomb of David is far off geographically, but it is the subject of a recent article that argues that it is authentic. Most who hold to the Mount Zion location being accurate are ultra-Orthodox Jews who follow tradition without regard for the evidence. This article, however, tries to make an intelligent case. It fails, but if I was teaching Jerusalem archaeology now, I’d require my students to critique it as a useful exercise in thinking about what we know and don’t know about ancient Jerusalem. I’m not going to comment on it myself, but if someone else takes up the challenge (and does a worthy job), I’ll either link to it or post it here.
UPDATE (8/6): Joe Lauer has mentioned below a previous article in the same publication on the tomb of David. This article, by Ari Zivotofsky, is worth reading for any who want to know more about the subject.