Finding the right bank for you depends strongly on what you will be using the bank for. For example someone looking for a consolidation or personal loan would want to concentrate on loan interestrates. While you can get a loan from banks you don't have an account with or a loan company, it is often easier to go to your home bank. It can also frequently lead to lower interest rates than a loan company. You may also be able to get a little more flexibility on personal loan amounts.
If the bank will mostly be used for checking and savings accounts you'll want to check interest rates on those accounts. Most banks will also have several perks, whether it be money or gifts, for enrolling in things like direct deposit, automatic bill pay and online banking. One thing to watch carefully when looking at bank accounts, other than the interest rates, is the minimum required balances. Banks will often have accounts that have great interest rates, but incredibly high required balances. This becomes less of a problem if the account will be used for a business or you are independently wealthy, but for most people a $20,000 balance is unrealistic.
With huge advances in online banking it has become incredibly easy to compare banking institutions. I recommend, however, actually going into the bank when opening the account. Often there are addition accounts available that may suit you better that were not listed online. Also there are often specials or perks going on you simply can't get online. Plus it gives you an idea of how far you will have to drive if you ever need to visit your bank. So basically, research your bank rather than just picking the closest whether you are there to open accounts or simply apply for loans.