There are several ways you can do this - all under different price tags, yet all a delightful experience.
1) $ - BYO. Go to the fish markets on the way and assemble a platter of your favourite seafoods. Take a picnic blanket and some wine, and sit in the park at Watsons Bay, or take in the views at The Gap. Open a bottle of crisp dry white wine and enjoy. Don't forget the wet wipes! Dodge the seagulls.
2) $$ - Watsons Bay Hotel. A Sydney icon, you can enjoy a seafood platter here, seated at tables and chairs and all the conveniences. A full bar is there, so no planning required. You still have to dodge the seagulls.
3) $$$ - Doyles on the Beach. Enjoy the same seafood, and more expensive wine, but with the luxury of table service. This is a more luxurious, long lunch setting, with uninterrupted water views. This experience comes under premium price.