Sonic Youth was the Velvets and The Fall; I found a list of setlists from '70s CBGB and made a playlist, and you can hear Sonic Youth all over it.
Throwing Muses (a favorite of mine) a little harder to pinpoint, feels to me like the product of a scene more than a direct evolution of clear antecedents, rather than an act like Dinosaur Jr. was a perversion of Neil Young. A good contrast to Nirvana.
PJ Harvey is the Pixies antecedents plus Patti Smith. People say Beefheart; I don't know Beefheart well enough to say and have a deep suspicion of people who bring up Beefheart.
Kate Bush is prog rock.
Einsturzende is Can (or like a violent response to Can).
The Cure is radio-friendly post-punk; their early stuff, which is the only stuff that comes close to holding up, is basically Wire.