The best song in the game is Hyrule Castle's theme and it is the only song from Breath of the Wild that left a strong impression on me, and is an outlier among the entire soundtrack. Phenomenal track and, in my opinion, is among one of the strongest in the series, up there with A Link to the Past's Dark World theme--which is one of my all-time favorites. The castle theme was a powerful and progressively arranged medley of multiple songs in the series, while also retaining its own identity as a Hyrule Castle theme. It's pacing was well suited for the atmosphere of the castle, and had a huge impact on my experience of going to the castle for the first time. It captures the mood excellently and the multiple channels was a subtle but very effective touch--and how the Legend of Zelda main theme layers overtop Zelda's Lullaby perfectly is an astounding feat on behalf of the composer.
As for the rest of the soundtrack, while the instrumentals were very well done in Breath of the Wild's soundtrack, it was very lacking in legitimate background music, and most of the soundtrack was just ambient noise with an occasional melody. Of the songs that were actually... songs... not very many of them were memorable, in my opinion. A lot of them were designed to be atmospheric, and that, they did well--as with the variation changes as you activate terminals inside a Divine Beast--but the songs themselves lack that character that I so strongly associate with Zelda songs. Again, the instrumentals were phenomenal, but the composure of the songs themselves felt very lacking in most cases as opposed to more iconic tunes from previous titles. Of the [original] songs in the game that I can think of that were not of the ambient variety, only two of them have a melody line that I can recall (one of them being Hyrule Castle), which is very disappointing when you look at songs like Ocarina of Time's Gerudo Valley and The Wind Waker's Dragon Roost Island and you can immediately hum them because they are distinct and individual. Yeah, Rito Village is a redux of Dragon Roost, doesn't really count because it's not original to Breath of the Wild--and, besides, The Wind Waker's rendition is far better anyway.
So, yeah, best song: Hyrule Castle. Some of the battle music, like the one that plays against Taluses, are somewhat noteworthy as well, but most of the soundtrack was designed purely to be background noise, and even full tracks just do not have my attention in this game.