I would say VII nailed it's atmosphere in large part due to the music as well. Not only is it one of the best soundtracks in the series, but almost every track is pitch perfect for the scenes it's used in. I think this one benefited a lot from the lack of technical limitations the PSX offered because it let Uematsu really just compose for each area and scene and no sacrifices really had to be made in terms of the number of compositions.
Though admittedly I think the art style worked heavily in its favour as well. The move to pre-rendered background helped on its own, but I liked that the areas in the game are rarely attempts to make photo realistic towns or villages. There's still some amount of exaggeration of their features, proportions not being quite right and that sort of thing which I think let them be a bit more creative in how they designed them whereas games like FFVIII and later on FFX or XIII strived more for that realistic graphical style that VII wasn't in a position to go for, but which can come off seeming kind of bland when not done right. VII's areas, while still quite detailed for the time are still simpler and less detailed than what came later and I think it made them cut to the heart of how each was supposed to look and feel whereas later games are sometimes losing that feeling in the little details to some extent, although they still have their share of great areas.
I'd also add my agreement that FFIX, XII, and I think VI as well had great atmosphere through out. IX for being the first to have an absolutely massive, detailed living world, and XII for being something of a progression of what we saw in IX. If IX pulled off a massive detailed world, then XII's was gargantuan and overflowing with characters, history, cities, ruins, etc. to discover and explore. There really is nothing else in the series that comes close.
And VI I think managed a remarkable amount of atmosphere for the time it came out and the technical limitations they had to overcome. It had a soundtrack that is easily equal to or better than VII's, and despite some repetition of certain songs, is usually dead on as well with the scenes they play in. Moreover, each town saw a big jump in number of NPC's from FFIV (FFV wasn't out when I originally played it), and despite re-using tile sets for pretty much every town, created a hell of a lot of unique layouts that I still distinctly remember to this day. You've also got individual scenes like the opera, traveling to Vector, the Espers escaping, everything leading up to the floating continent and the World of Ruin which are permanently seared into my memory because they're so epic, and not to go unmentioned, the complete shift in tone for the game when you awake to the WoR. That almost overwhelming sense of hopelessness. That even as you struggle on you can't help but question why. What is left to save, and can the world ever recover? When we win will we just slowly die anyway? The last half of the game is positively dripping atmosphere.