I am US green card holder in Maryland. I found a job( internship) in NYC. Can I open a bank account in NYC? If yes what documents I need to open an account there.
There's nothing that forbids you from opening whatever accounts you want wherever you want them. You don't even have to have any legal status at all, but you do need to have a proof of identity.
That said - what does it matter where you opened a bank account? Most banks allow services over the phone/email/web/apps, and those that don't - don't open an account there. The only consideration should be the ATM networks and fees, and most small local banks participate in one of the National ATM networks.