You need iTunes at the very least to set up your phone. You can't activate your phone without plugging it into a computer and iTunes. You might be able to get the store to do this though.
Ok let me rephrase that.
I'm sitting in a park with my iphone downloading apps, drinking beer, looking at girls, downloading movies all using just my iphone, nowhere near any computer, worry free, until cows come home. Can i do that or should i buy android phone instead?