I used Tompkins Trust when I was in school up in Ithaca. They are a very good local bank. They have a lot of special programs for students that make it easy to bank there. They waive the minimum balance requirement during the summer months when you are away.
They have ATM locations all around Ithaca including Collegetown, the Commons, and downtown.
Their interest rates are not great, but they are the same as most banks nowadays.
I had no problem getting a credit card from them and they have been good about raising my credit limit.
Although they don't give free online bill pay, you do have free online banking so you can check your accounts, transfer money, and change your information online.
Since they are a local bank, the downside is for those who live permanently somewhere far away. You don't have ATM's near you and are forced to pay the ATM surcharge to withdraw money.