Funny, I absolutely adore Radiohead, Blur, and Bjork. I used to really be into Pink Floyd, but now most of their music makes me ill, especially Wish You Were Here and The Wall, less so with Dark Side of the Moon. I still really like Piper at the Gates of Dawn, Meddle, and Animals, and I can deal with the minor ones (Atom Heart Mother, Obscured by Clouds, etc.)
But, to address the OP.
Live, Weezer, the Dave Matthews Band, Sarah McLaughlin, Natalie Merchant/10,000 Maniacs. I can respect their styles and musicianship. It is just that their songwriting kind of runs next to my tastes – they write lots of songs that I almost but not quite like (but of course my wife loves all of them).
TMBG drives me up a wall but I wouldn’t classify them as a “best” band.