You might enjoy A Bright Shining Lie - John Paul Van and the American War in Vietnam by Neil Sheehan, a colleague of Halberstam's during the early part of the Vietnam War. It covers the early part of the Vietnam War, through the lens of US adviser to the RVN John Paul Van.

Another colleague of Halberstam's was Michael Herr, who wrote Dispatches (I think it's a collection of reports he filed during the war). More of an impressionistic picture of the war, less of a history. You might recognize some of the scenes from the film Apocalypse Now from this book (IIRC, it was a while since I read it).

Not a history of the war, but William W. Prochnau's Once Upon a Distant War is a story about the young journalists (Halberstam among them) who caused the US government so much grief through their reporting on the Vietnam War. Find out why some called it "Halberstam's War".