If you want service at a local branch, I would look into local Credit Unions that you can join. I belong to one in Michigan that I qualified for years ago, but I currently live in California. It is very easy to work with them since their membership is limited. The fees and minimums are far lower than any bank (mine has free checking and savings with a minimum $5 balance). There are a few ATM networks that are free for my CU, and most are part of at least one. This means that I can also do deposits at the machines that will take them, however my CU app just added mobile deposits.
The savings rate is pretty horrible (0.21%), however it is easy to link a non-brick and mortar bank to your CU, if you wanted your savings to be a little less accessible. I only keep a couple thousand in this account for monthly expenses, and everything else is drawn from it to higher rate savings and my Vanguard account automatically.