Of course it's worth it! Istanbul has an amazing restaurant scene.
Very close to the airport (albeit in the ``wrong'' direction if you're heading downtown), actually doable on a relatively short layover, is one of Istanbul's best traditional restaurants, Beyti. It's so famous that their signature kebab has a wikipedia entry.
If you're going downtown and have time for a nice dinner, there are several places that serve a modern take on the traditional Turkish cuisine. I recommend Yeni Loanta and, even more, Neolokal.
Finally, if you get to Asia, don't miss Ciya.
For breakfast, I would simply go to Bahcelievler and pick a nice burek spot... It's 2-3 stops on the metro and very accessible.
Enjoy!