I recommend that you have at least an account at a Credit Union of your choice, perferrably the Credit Union affilicated with your university and / or your company. The reason is that Credit Union usually offers lower fee and better loan rate, since they know who you are and what to expect from you. For example, I get much better ATM fee (zero) on international travel from my Credit Union than from my account at a national bank (not to name the name).
You should also have at least an account at a national bank, such as Bank of America, WellsFargo, Citi, Chase. You can get much wider range of service and much wider banking network from those banks.
Most of the mortgage allows you to pay online from any checking account from any bank for free. However, there are some mortgage that does not allow that. In this case, you better open a bank account at that mortgage.
You also want to select one bank for your wealth management. Personally I like MorganStanley SmithBarney, simply I like the financial advisor I worked with for a long time. Choose your financial advisor carefully, and go with him/her.
That would pretty much settle the banking business. The decision you make is mostly likely depends on the local branch and financial advisor.
