Uhm, you know that it doesn’t exist only alternative rock, do you? Also, alternative rock cover a large amount of types of rock like indie rock, punk, indie pop, and so on, just like it exist alternative metal, alternative rap, and many others.
You should be more specific of what you’re searching at. I can suggest, you like others said, Evanecence just like the Gogol Bordello, that are completely different (but they are amazing, try hearing Pala Tute).
Well, talking about indie rock, it’s actually a genre that I prefer. I hear most of groups of this genre, or relatively alternative, so I can suggest you some. Let’s see other groups that I know… You can try to listen at the Ok GO, Gorillaz, The Cardigans, Imagine Dragons (Monster and Demons are the best!), Die Antwoord (even thouth this group is alternative Rap), and The Ting Tings.
Let me know if you tried them out, I like a lot all of this groups!