Interest rates are on the rise so if you have savings or are planning to open a Certificate of Deposit account (CD) take a look at some of the banks offering good rates. Ally Bank and Discover online savings rates are usually higher than banks with local locations. There's no reason that you can't keep a checking account locally (as long as there are no fees involved) and use online banks for savings, money market and CDs.
Bankrate is a good site to compare interest rates, and also mortgages.
Note: Make sure you are comparing both the saving rates and if interest is compounded. Some banks don't add the interest until the end of the term whereas others add interest monthly or quarterly so you're actually accruing more on both the interest and your principal amount combined.