Ash, how long are you going for? In two full weeks of evening meals in July, we only managed two tavernas twice - Brouklis where were staying and Efihithia. Both times because we were meeting others on the second time. We didn't manage to get to Horizon, Marina, Portofino, Captain's Table, Rainbow, Stekis, Mirage..... You would need a month to try everywhere.
As for the "whale" I haven't mentioned all the lunch times.. I've been on a diet ever since we got back!!
Have a great time
Phil