"Bloodletting (The Vampire Song)" is probably the one song most people are familiar with, or "God Is A Bullet" or "Caroline".
I did the stage monitor mix for a Concrete Blonde show last year, and they were great live. I was never a fan of the records, but their live performance won me over. They are a three-piece band, just guitar bass and drums. The bassist is the lead singer, and is a girl, Johnette Napolitano. She's got a killer set of pipes, one of THE great rock voices. The guitarist, Jim Mankey, is also quite good.
The height of Concrete Blonde's popularity was the late 1980s/early 1990s, and they either broke up or took a break after that, but re-formed a couple of years ago. There's a new album or two, and the new material is quite good. If you can find the "Live In Brazil" album they released a couple of years ago, that will give you an idea of what to expect from their live set. If you are very lucky, she'll throw in a cover of Leonard Cohen's "Everybody Knows" that will make your spine tingle. When I did them, the sound check was a cover of The Bee Gees' "To Love Somebody" that she did with a totally straight face, no irony, and it was wonderful; I don't know if it's part of their live repertoire or if they were just goofing around.