I've had online accounts since back in the early days when you could get 5% interest. Those days are gone. Now you're lucky to get 1% in a savings account, much less in checking.
Given the low-rate environment, consider convenience as well as yield. For example, Capital One 360 pays 0.20% on their checking account. If you keep an average of $5k in there, that's $10/year in interest. If they truly offer every service you would ever want out of a checking account, you might as well pick them. If a brick-and-mortar bank or credit union would provide services you value at even $11/year, ignore the interest and pick something else.