Lotty I have eaten at many of the restaurants in the fish market some of them quite recently and found all bar one to be very good. When Doğan and I go together we always go to Cem Can which we discovered years ago partly from loyalty like you but I like the fact they serve the extra plate of rocket (my favourite) as well as the salad and they serve fresh home made bread unlike most of the others who serve the daily bread.
I also like their mezes in particular their smoked aubergine and seaweed mezes and the octopus and olive meze is simply delicious. The service is good and of course we know the staff there quite well now.
When I go with friends I get the chance to try other places although always a bit conscious about being spotted!!!
Recep's and the one on the left hand corner just before you enter the vegetable market are both good.
There is just one place I'm not keen on as I found the mezes selection limited and not available to view being made only to order and what we had was tasteless and I didn't like my main fish meal
and I was served tap water which is a sin of the highest order in my book instead of bottled water which I noticed immediately upon drinking it.
But I do love the atmosphere of the fish market and considering it is a bit pricey there are always lots of Turkish people eating there.
We have also visited Girida (the fisherman's cooperative on the opposite side of the road just up from Shaka) twice now and just have a selection of fish and other mezes - no fish main meal because as has been reported on another topic is expensive at 70TL per kilo for sea bream for example and have really enjoyed our meals there.
We did ask the price of all the mezes which range from about 5-18TL the first time we went in fear of being taken advantage of but they seemed fairly reasonable.
The service at Girida is excellent too so it may be worth considering trying there if you fancy a change without being spotted