1. Chase — Headquartered in Manhattan, branches in all five boroughs, Manhattan
The default New York bank: more branches and ATMs in the city than anyone else.
JPMorgan Chase is headquartered in New York and banks the city accordingly. There are Chase branches in neighborhoods where no other bank has bothered for years, the ATM network is the densest in the five boroughs, and the app is among the better ones at this scale.
What you pay for that is a fee schedule written for a bank that does not need to compete on price. The monthly fee is waivable with direct deposit or a minimum balance, so for a salaried New Yorker it is effectively free — and for someone whose balance runs low at the end of the month, it is the most expensive option on this list.
Good to know: Set up direct deposit on day one. It is usually the simplest route to waiving the monthly fee, and it is easy to forget after a job change.