One of my all time favorite bands!
I love them in all their various incarnations.
My favorite albums happen to be the ones that @berner99 is referring to as "nasty stuff": Larks’ Tongues in Aspic, Starless and Bible Black, and Red. I love angular sounding music, as well as the more obviously beautiful sounding stuff, too.
Others have already said, their first 4 albums are the call. The title track from the album "Islands" is quite mellow, and has maybe their most beautiful melodies of all their albums.
I happen not to think any of their stuff is ’nasty sounding’, though. There is a certain beauty to those dark, intense, dissonant sounding pieces. It’s just a beauty that is not obvious, and may take a bit of ’work’ to understand and appreciate.
But then, I love post 1950’s atonal classical music, which can make even the most angular ’nasty’ King Crimson stuff sound like it’s very mellow and melodic 😉
Might I go out on a limb here, and recommend the Italian prog* band, PFM? Especially their first 2 albums, Storia di un Minuto, and Per un Amico.
They are much in the vein of the more mellow, beautiful, and melodic King Crimson pieces. But they are not a ripping them off, they are doing their own thing.
*Italian prog on the whole, is very close to the quality of the Brits. Sadly, it is now somewhat unknown to people getting into prog at a later time.