Half of my money in Ally, the other half in Barclays Online. (Both offer around 1% savings accounts, among the highest in the business.) Schwab is my go-to ATM

Half of my money in Ally, the other half in Barclays Online. (Both offer around 1% savings accounts, among the highest in the business.) Schwab is my go-to ATM account, since it offers reimbursements on all ATM fees, including the 1% VISA tax, even abroad. Moreover, they're very good with not blocking your card: I called them once, they put my card in "training mode", and it's worked flawlessly in about 10 countries since. Ally also has an ATM card that works abroad, but it has the VISA 1% and only offers reimbursements in the US. Both Ally and Barclays offer free ACH transfers. I also use Vanguard for a few investments. None of my banks have physical branches abroad, but this does not bother me. I also don't have to cash foreign checks or accept deposits from foreign banks, which may be a problem for you. I don't believe that Ally accepts international wire transfers, for example. I've been using this system in Europe for about half a year.