I use Schwab for brokerage and checking. They have a great global ATM fee reimbursement (you essentially never have to worry about pulling cash from any ATM, anywhere). They also have some of the better technology to support their services that I've seen (mobile apps, 2FA, TouchID support, etc).

I also recommend a separate account in Ally Bank for an emergency-fund because they have a great high-yield 1.20% interest rate saving account. The catch is that they're online-only, but that's fine since it'll only be used for emergency assets.