I've had my checking account with Schwab and savings with Discover for about a decade at this point. The former is all mobile deposit, but they refund ATM fees anywhere in the world. The latter has a variable interest rate which is currently at 3.3%. It's not always the TOP interest rate, but it's always right there (and is a hell of a lot better than you'll get at any traditional bank).
The only downside is the extremely rare times when you have a bunch of cash that you need to deposit, so I ended up opening up a savings account with Chase (which has a branch about a quarter mile from me) and just parking $1k in it. I've only needed it a time or two, but it's nice to have the option.
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