If that's the experience that you want (ie: picking out a fish and having it prepared for you simply and excellently), and you're not locked into it being a Greek place in Astoria, you might try:
24-25 Steinway St
Astoria, NY 11103
Phone: (718) 721-9010
Egyptian, with a relatively small menu; they'll grill or oven-bake a fish of your choosing and bring it to you with pita, olives, and lemon -- it's fresh and wonderful stuff.
dont waste your time on elias. hasnt been good for many years. kyclades is the place to go. really fresh, friendly service excellent food. i go there all the time and always recommend to friends. have 2 sets of friends that live in new jersey who make the trip just to go to kyclades. give it a try-you wont be disappointed.
I would recommend Agnanti (Ditmars & 19th) right by Astoria Park. Wonderful fresh fish, reasonable prices and delish preparations. Just be warned of the long wait for a table on a Friday or Saturday night, even with a reservation. Would suggest going at a bit of an off hour/day to avoid the crowd.
I have also heard very good things about Kyclades (sp?) on Ditmars and 33rd/34th (right next to Top Tomato). I haven't eaten there personally. Not sure if there's a display of the fish there.