Many smaller community-based banks and credit unions will allow you to open a checking account and access a number of other financial services and products with an ITIN.
Here are a couple places to get started with finding the right bank or credit union for you.
Juntos Avanzamos: Credit unions that are part of the Juntos Avanzamos community are committed to expanding financial services to immigrant communities. These credit unions accept ITINs as a valid identification number.
BankOn: Accounts that are certified by Bank On meet certain banking standards that ensure that everyone has access to a safe and reliable account. Though you’ll want to confirm with the bank itself, most of these accounts are available to ITIN holders.