Flying to Azores is very easy these days as the airport has been upgraded for several times allowing for larger airplanes and even low cost airlines are flying already to Ponta Delgada International Airport.
Being an archipelago in the middle of the Atlantic Ocean it means a longer flight distance but warm weather, great surfing conditions and nature are worth the extra hour or so.
Only a few airlines fly to Azores. There are a few direct flights from Europe and US to Ponta Delgada airport. Check out some of the flight companies flying to Azores, Ponta Delgada airport:
Sao Miguel Island (Ponta Delgada Airport)
Air Berlin http://www.airberlin.com
Sata International http://www.sata.pt