A song like Beautiful Day could be U2 Beginner's Level. (I'm speaking of the listener level, not the band). It's super catchy and easy to like, even for those who have never heard of the band. It probably translates really well outside of the English speaking world, too.
On the other end of the spectrum is the ability to appreciate excellent songs that you would never start somebody out with. These songs will not be understood or enjoyed by people at a beginner, intermediate, or maybe even advanced level of U2 appreciation.
Nominate some songs for this level. Here are three from me.
Miami
Grating, almost atonal, seemingly vapid lyrics. The genius that is Miami is pretty hard to grasp.
Elvis Presley and America
It sounds like a song done in one take because that's precisely what it is. Imagine playing this for your coworker or neighbor. Um, no. But jesus, it sure is something.
Wake Up Dead Man
Mumbled, distorted vocals. "Jesus" in a rock song, repeatedly. Disorder in the music. Awesome, sign me up.