Songs to cover for modern folk band?

So I'm really into bands like Fleet Foxes and The Civil Wars. After watching The Civil Wars Disarm cover, we really wanted to do something similar, like taking a song by a band like The Smashing Pumpkins or other bands (RHCP, Radiohead, etc.) It doesn't have to be limited to those bands, just examples. Anyway, we have a keyboard, guitar, kickdrum, djembe, harmonica, mandolin, melodica, uke and who knows what else. We just really want to do this, please give suggestions!