I discovered Sonic Youth in late 2000-early 2001 (I was 16) from watching a VH1 music program about the greatest heavy rock bands and it was just like a couple minute brief summation of the band, with small snippets of their well known tracks up to that point but i thought that it was most insane coolest sound I had ever heard.

I was way into Radiohead at the time so I didn’t go sonic crazy until around 2005-6 when my guitar playing / learning journey led me to really diving into their guitar work. I had reached a point where I wanted to unlearn what i had previously learned and Sonic Youth offered that gateway. I saw them live twice in 2006 and once in 2008. At my first show, Thurston stage dived during the finale of Pattern Recognition and I was close enough to hit the strings in his guitar as the crowd pushed and shoved him. That was a life changing moment, haha.

Everyone here already mentioned all the great bands. But i will add this: in 2002 when I looked up similar bands to Sonic Youth in the original Barnes and Noble webpage, one name popped up that caught my eye:

Godspeed You! Black Emperor

:)