I use a local credit union for some banking.
Citibank for an online savings account. I like that they allow for sub-accounts for different goals.
Schwab for online checking, savings, investments...this is where my paycheck gets direct deposited.
Fidelity for 401K
I have been very pleased with Schwab checking. Never had a single problem with them and as JC mentioned, I can use any ATM...while I do get charged the fee at withdrawal, the fee is credited back at month end. I think I have been with Schwab checking for 10 years now.