Can you transfer data from an old iphone to a new one with itunes?

I've had an iphone 4 for a while now without being paired to an itunes (my old computer was stolen and I haven't had a need for itunes). How would I go about purchasing a new iphone and keeping my contacts/music, etc without backing everything up with itunes? I have an itunes account, just no actual computer with itunes. Can this be done through icloud?

I think you'll need a computer to back up your iphone.