Kiplinger's 2023 list of the best internet banks. Best National BanksBest Credit UnionsBest Banks for High-Net-Worth ClientsBest Banks for RetireesBest Banks for Families With Kids Axos Bank Why it won: From specialized accounts for teens and seniors to a high-yield option, Axos offers a free checking account to fit almost any need.Standout account: Rewards Checking yields up to 3.3% for those who meet certain requirements.The menu of free checking accounts from Axos includes the basic Essential