Agree with others who mentioned online banks for better rates. I've been using Ally for years, their savings account is at 3.5% right now, with CDs a bit higher.

I do still bank locally for emergencies, larger cash withdrawals, or certified checks. I've been with Mutual Security Credit Union for over 10 years and have never had a problem. Not sure where you are, but they're around Fairfield, Litchfield, and New Haven counties.