How I View It
> yes i do have sonic youth in my collection and im not throwing it away. if
> you trace the roots of sonic youth youll start w/ the velvet underground
> w/c would link to the jesus and mary chain then the cure and will end up
> to the smiths.
The Velvet Underground is the common root for almost all of the bands that flourished in the 1980s, so starting there is almost meaningless.
However.
The more direct connection is the Velvet Underground to Lou Reed solo to Patti Smith/Marc Bolan/David Bowie to Morrissey. And of course there's Morrissey's quiet fascination with Nico. I don't think Marr was terribly interested in the Velvets. With him you'd start with Roger McGuinn and Motown, I think. He has gone on record as saying that punk meant very little to him.
The daisychain of influence leading to The Smiths is wrong as you have it. Jumping from The Cure to The Smiths is a gross error. However it may sound to casual fans of both bands, The Smiths were in fact a hundred million miles away from The Cure, and certainly were never influenced by them (unless you mean in a negative way).
I wouldn't know how to describe the sources of The Cure, except to say that had Bernard Sumner, Ian Curtis, Peter Hook and Stephen Morris (and later Gillian Gilbert) not started a band, "Fat Bob" would have spent his life toiling in a wig factory mumbling Baudelaire to arthritic octagenarians.
Also, while the Jesus and Mary Chain owe a lot to the Velvets, they are equally indebted to Echo And The Bunnymen, who themselves may be linked to VU, Television, Bowie and The Doors.
Any similarities or parallels between The Smiths and Sonic Youth would be strenuously denied by both parties, but I suppose it's fun for fans to speculate.
Indeed, part of the fun of enjoying both the U.S. and U.K. music scenes between, say, 1966 and 1990, is that the music was unique and not always related to its ostensible counterpart across the Atlantic. For instance, a lot of American punk fans loathe British punk rock, and no doubt their hatred is reciprocated. Years later, grunge came along in the States but didn't have as big an impact in England: Madchester was heating up. So liking bands like Sonic Youth *and* The Smiths was a treat because you weren't just getting more of the same. Instead you had two different strands of indie music that were totally different though somewhat similar in spirit. That's really the true link-- independence from corporations.
Or alleged independence, if you like.