It would be extremely incorrect to narrow Sonic Youth down to just their classics, but let's start there for now and see how it goes.
Noise rock exists in part because Sister does; because Daydream Nation does; because EVOL does. Three records here, with awkward, alternative tunings, that really forced people to call punk rock "art". They jangled their guitars in new, discordant ways, mumble-shouted over structureless designs and refined harshness into a palatable, songful world. Those are their classics, though you might argue Kim Gordon and Thurston Moore also struck gold with records like the more traditional Goo and the disquietly no wave Bad Moon Rising.
They continued to make pleasing, subliminally experimental alt rock for years -- beyond that story, though, Sonic Youth started dabbling and never looked back, trying out new things in their SYR series in a headfirst embrace of the avant-garde. As if they were a band full of Glenn Brancas, they made improvised shred records, inviting musicians like Jim O'Rourke, Merzbow and Mats Gustaffson to join in. Fully embracing non-linear structures and unwanted sounds, this series marked the inventive and uncompromising sound of Sonic Youth, suggesting they could do pretty much anything they wanted with rock music -- they could destroy it completely, and it might still rule.