I've been using Bank of Arizona for over 1.5 years now for my small business. They were the ONLY bank in Scottsdale/the east valley that doesn't charge ANY fees and have absurdly small minimum account balance requirements (e.g. I think I opened my account with $50 and have never been charged a fee. Ever. Nor will I ever).
They may not have the fanciest branches, nor a bunch of them, but they are friendly and take care of me on the rare occasion I need to do any in-person banking.
Warning: they also have shorter hours than most banks, but the cost savings to maintain an account make it easy to justify a minor inconvenience.
Highly recommend!