I ate at Baccalao this evening, I'm afraid it was extremely disappointing. Had the calamari fried with onion and garlic and the caribou main. The calamari was tough and a touch greasy, and the caribou, while a beautiful piece of meat, was absolutely murdered by the partridgeberry sauce. The vinegar overpowered everything else. There were also some amateur gnocchi and fall veggies. I hope you have a better experience!
I second the suggestion of Baccalao. Benn twice and cannot wait to go back to SJ for a third. Bianca's was good too, but not as local focused. it was nice being a lone diner to sit at their open kitchen bar and talk to the cook staff.
One of my favourites is about a 20 minute drive from downtown in Portugal Cove called Atlantica. right on the coast on a cliff overlooking the water. Bit more formal than you might be looking for. I went casual, but most were in suits and dresses. The service and the room were chilly, but the food was excellent.
Don't overlook Magnum & Stein's or Bianca's:
The latter is more fancy restaurant than casual bistro, but it's not ridiculously so. Both tend to feature a few dishes that feature local seafood. Bianca's also often has caribou, a delightful game meat if you've never tried it.
Basho, a restaurant run by a Newfoundlander with Japanese roots, is also a delightful spot. You will not be chowing down on local cuisine, though. Local ingredients? Yes. Local cuisine? No.
I just posted my review from my recent trip there: http://chowhound.chow.com/topics/652987
I'd recommend Blue on Water (very local), Baccalao (focus on locally sourced food with an emphasis on newfie cuisine - local art and music in the restaurant too). I heard good things about Aqua too but we never made it out there.
I live away from home nowadays, but last time I was home I had lunch at the Yellow Belly Brewery and was very impressed, as I was sort of expecting standard pub fare. Nearby diner's meals looked equally impressive.
If you want a fantastic view for dinner, or lunch even (which is when I was there), check out the restaurant at The Rooms and try to wrangle a seat near the windows.
Another lunch recommendation, if you have time to yourself , and are staying at the Fairmont or area, Sun Sushi is just a "hop, skip and a jump" from there.
India Gate is also great, downtown.
I also hear very good things from family and friends about Blue on Water and they have a few local specialties.
as well as
which is described as Nouvelle Newfoundland cuisine.
and the Gypsy Tea Room in the old Murray Premises building. There are loads of great places in the downtown area.