Staying in the Dorsoduro (my favorite area and a great location) you'll be spoilt for choice. For a more local Venetian feel head towards San Barnaba and Campo Santa Margherita. If you do a search on here you'll find a lot of recommendations for special places. Knowing the Hotel American I'm sure they would even be able to recommend something as well. Enjoy Venice - even in the dead of winter it's spectactular.

If price is no object, then I think about the best are
Antico Martini
restaurant of the Cipriani hotel
Da Fiori

However, these very special occasion places are not frequented by that many Venetians on a regular basis, especially a hotel restaurant.

I have a long file on Venice, if you'd like to see them, email me.

Just got back and had a wonderful time even though we got aqua alta (floods at high tide) each day. Would strongly suggest Ai Gondolieri in Dorsoduro for a great "special meal." Their wine list is outstanding too if that is of interest. We also tried Bacaro Jazz(sp?) near the Rialto Bridge in San Marco, but just for cichetti (sp) and wine. Had a wonderful plate of mixed seafood to share and good wine by the glass. This plus another wine bar for mixed cheeses and more wine plus dessert on street was a great way for a lighter dinner, but finding places that locals eat. Have fun and explore - sometimes just choosing by the menu or by hotel suggestions is great. We also stayed at the American several years ago and found them to be helpful with suggestions.

Cantina do Spade

www.dospadevenezia.it/

One of the best meals we had in Italy. Our B&B owner took us.