Always exchange currency at the bank. At the airport, they would charge higher exchange rate, that is, of course, if you could even find a location that would even offer the service.
Both work. The service charge at the airport tends to be higher than the one charged by banks. Most credit cards also now have a service charge in addition to the exchange rate. Airport tellers often have a broader range of currencies available though, so they might be a better choice if you're traveling to an unusual area.
You are better to exchange currency at your local bank as it will probably be cheaper. Just make sure to let them know ahead of time to make sure they can do it.