So, as someone whose background is more in the arts, I find that the works of history I tend to gravitate toward are works that are well-written. Gibbon's work is, of course, the most famous work of "history that's just damned good writing", but there have been others that have taken up his banner. Will Durant's "Story of Civilization" is a deeply engrossing read, for example, and his ability to distill historical persons and events down to a few concise, musical, funny, and memorable lines or paragraphs is nonpareil. Winston Churchill exhibited "sturm und drang" like few other writers of history before or since. Daniel Boorstin was probably the best of the lot, his two famous trilogies - the "Knowledge Trilogy", and the "Americans" trilogy - being well-organized and -crafted works whose depiction of historical figures are colorful, well-rounded, and give them with a greater measure of depth and realism than most other writers of history.
However, at the same time, I'm not blind to these writers' deficiencies. Gibbon's ahistorical excesses are broadly acknowledged, Durant was working in a field that wasn't really "his", Churchill played loose with facts and had an obvious ideological and personal agenda he wished to get across in his histories. Only Boorstin seems, to me, to have been a pretty well-respected historian, and even then, I'm sure he has his detractors.
Conversely, from what I have seen, many of what are considered to be the "best" works of history on particular eras seem, well, rather dull - interesting facts conveyed with all the vivacity and fun of a lecture on tax law. Either that, or you get writing that tries to be interesting, but ends up being melodramatic and silly, a la Shelby Foote.
It seems to me, then, that there is a niche in the middle - for works that are more rigorous in terms of their history, while still being well-written in terms of their prose and well-crafted in terms of the historical narratives they weave. I have read at least one work that I think is a good example of this - Richard Rhodes' "The Making of the Atomic Bomb", which is a truly excellent book, in terms of the way it weaves copiously-researched accounts of the factual events it covers with very dimensional, nuanced characterizations that grounds the actors in the political, philosophical, scientific, and spiritual zeitgeist of the era being written about - but what are some others that are similarly meritorious?
What constitutes a "good writer" is completely subjective. That said, Ronald Syme's books on Augustus and Tacitus (I think they are in the reading list) are about as literary as modern historiography gets.
It's been a decade since I've read Syme's book on Tacitus, but the English smacks of Tacitus' Latin style. And his Roman Revolution is an absolute classic.
Aside from that, I like Meier's biography of Caesar, even though it's translated into English, and it's hard to go wrong with the classics themselves. I'm not a great fan of Livy, but Sallust and Tacitus are fantastic, both in Latin and in translation.
Anything by good old J. J. Norwich
Barbara Tuchman is a wonderful writer, and I'm defining "wonderful" as both intellectually rigorous and able to tell a story in a satisfying narrative and stylistic way. Her Guns of August is a rich account of the lead-up and early days of the First World War. I also really enjoyed the writing in Timothy Snyder's The Red Prince, which is a history of the transitions in Eastern Europe from the 1900s-1950s posing as a biography of the picaresque Archduke Wilhelm (Wilhelm Franz von Habsburg).
Thanks for the answers, all. Was hoping for a few more, but these seem like a good start.
Will Durant in my opinion is the best "storyteller" that I have read. His history of Rome, Caesar and Christ is an incredibly detailed and comprehensive history of Rome from the beginning to the end that is never boring. One thing is that he tends to focus on social and cultural aspects and a little less on military matters although he doesn't ignore them altogether.