Nagasaki is the closest airport, but there are very few flights there and what flights there are tend go be expensive. There are a greater number of flights - often at discount prices - in Fukuoka. It is very easy to get to Sasebo from either Nagasaki or Fukuoka -- by train or highway bus. Enjoy -- it's a wonderful place to visit!!!
The nearest airport is Nagasaki, in Omuru Bay. You can get to Sasebo from there by bus (30-60 min.)