I haven't lived there for a while, but I can fill you in on generalities.
Qingdao features Shandong food. Qingdao itself is known for its seafood, especially little clams known as gala 蛤喇, and for dishes with sea cucumber, crabs, fish, etc. Of course the beer 青岛啤酒 is rather famous, and in Qingdao you can find tastier varieties than just the plain old watery Qingdao available throughout China and the West. There are also some great Uyghur style restaurants. You can check out the expat "redstar" magazine online for some local tips, but in general I found the quality of food in QIngdao to be quite high, so don't be afraid to walk into any old place that seems popular with the locals.