Nell (indie rock. Awesome), No brain.
I also like Mary Story, My aunt Mary, Izy (beware of Engrish), but they're maybe a bit less rock-ish and more pop-ish? Hmm. Dear Cloud and Cloud Cuckoo Land -both two of my favorites- are more indie, imho.
I suggest you go to last.fm and run a search there. You'll see lots of recs based on similar bands/singers.