Restaurants in Paris

Dear friends,

I'm going to Paris for the first time next week, to spend four days in town. I have read a lot about the city and the tourist spots to visit and take pictures, but I find the best part of traveling is in trying out the local cuisine. I was wondering if you guys would be so kind as to recommend some nice places to go. All I'm looking for are nice places with good food. I really want to avoid the tourist trap, and I loathe having to ask the hotel concierge for help, for I invariably end up in overpriced, mediocre places.

Any help will be appreciated. I'm arriving in Paris on the 15th and leaving on the 20th. There are a couple of restaurants that have been highly recommended by my friends, like the restaurant on top of the Pompidou Center, but my list is currently too short for the number of days I'll be staying.

Oh, I'll stay at a hotel close to the Eiffel Tower.

Cheers!
Renata