Mortgage rates/fees go for a local credit union. For savings account rates go to local credit union or online bank with a high yield. Personally I have relationships with multiple banks:
Large National Bank with a lot of brick & mortar locations - I personally like walking physically into a bank and being able to obtain a certified check or other services. I keep a small amount in this bank for quick access to cash.
Local Credit Union - Benefits of a credit union which typically has higher interest rates on savings accounts. Also there is more flexibility and lower rates when it comes to loans then the national banks.
Online Bank - I run my checking out of this bank and also is where a majority of my savings are due to the high interest rates.
I also think it would be smart to run your checking out of a local credit union or small local bank but that isn't currently part of my strategy.
