We ate at Shell's twice during our recent trip to Port Aransas. Though expensive (meal for 2 runs about $50-$60 not counting alcohol), the food is truly excellent and gourmet.
On our first visit, I got duck breast and my friend got amberjack. The second time, I got scallops sandwiches with sausage and mint sauce, and my friend got grouper. The fish dishes are more generously sized than the duck or shellfish dishes, so you may want to take that into account when you make your selection. From what I observed, the pasta dishes are huge!
We also tried the salads (huge and very good) and banana cheese cake (great).
I wouldn't come here with young kids, but Shell's is a great place to go for a lovely and sophisticated meal -- and you wear your shorts and t-shirts!