I suggest checking out (no pun intended) Key Bank, if it has a presence in NYC. It is one of the big banks, but seems to have avoided a lot of the negative publicity so craved by BoA or Chase or Wells Fargo. It does not charge a monthly fee to use your debit card.
Credit unions are a good alternative, but they are not entirely perfect either. Many, like BoA in your case, want you to apply for loans online. After laboriously entering everything in, you get an email telling you a loan specialist will be looking at your application. Soon you get a phone call from this specialist who then wants you to make and send copies of pay stubs, stock statements, mortgage information, debt information etc etc etc. Then a loan committee gets together (at a time of their convenience, not yours) to decide on your fate. They are not always customer friendly; they slavishly and mechanically follow some rules from the NCUA (National Credit Union Association).
In any event, may I also suggest getting a "no annual fee" credit card with a low interest rate. If you pay off your credit card each month, you are essentially getting a free loan, and building up good credit at the same time. Some cards are attached to mileage plans so it comes in handy to build miles. I used my credit card for everything and managed to fly (for two) roundtrip to NRT a few years ago, and ready to do so again next year.
Like a lot of people, I believe BoA is evil and corrupt. They think nothing of sticking it to the customers on one hand and accepting a taxpayer bailout on the other. It's disgusting. Everyone who has an account with BoA should close it immediately and move someplace else. No corporation is too big to fail. None. It would make my day to see BoA finally close down.