I've been using Schwab for almost 8 years now and love it. They will connect with Mint. No sizable interest to speak of, but everything I need is free, including the following:
1) electronic transfers to and from other banks
2) check deposits via their mobile app (you just take a picture)
3) all atm fees refunded, including internationally <- this is a big one, and super convenient when I need cash
I've also heard many people speak highly of Ally, so perhaps someone with an account there will share.