Not very difficult. Ideally, an LLC’s bank account should be opened in the state where the business is operating and at least one of the LLC members resides. If you are operating in more than one state or have members who reside in different states, then it makes sense to use a larger bank with offices and branches in those states. Or another option, as you stated, is to open an online account.
Banks will not allow you to open a business account without first having your Articles of Incorporation. If you’re fortunate enough to live in a state where you can incorporate online, then you can usually print out the Articles immediately and bring them with you to the bank. Otherwise, you might need to wait a few days. In addition, banks will require you to have an EIN, which you can obtain immediately online by going to this IRS site. You must have both the Articles of Incorporation and the business’ EIN in order to open an account.
If you open up a bank account for your LLC in New York you’ll likely need an Operating Agreement as well. Unlike Delaware, New York requires LLCs to maintain an Operating Agreement so there’s a good chance banks within the state also require it.