This is what I was going to suggest as well.
Your backup plan is good too - you can't go wrong with Shaw's.
I agree with both these posts.
Here are a few tips about GT Fish. The menu is "small plates" (smallish portions, smallish prices) so you can have as much or as little as you like, in whatever order you like. It's one of those places that's both casual and elegant at the same time, if you know what I mean. It's also very popular, and often fills up with reservations in advance, so you'll want to make a reservation as soon as you know you want to go there. They're on Opentable.com so you can check availability easily.
Shaw's is still very good as well. In addition to lunch and dinner, they do a great Sunday brunch buffet. It's not cheap ($48) but it's all-you-can-eat, with seafood specialties like crab cakes, hot and cold shrimp, etc, as well as a carving station, great desserts (I still think their creme brulee is the best in the city, and they do a kick-ass chocolate pot de creme), and of course the usual breakfast specialties like benedicts and thick-cut caramelized bacon. They too can fill up, so reservations are recommended.
I ate at Catch 35 during Restaurant Week last year and was disappointed, so I would stick to these two instead.