Some suggestions.

Get the following books:
Food Lovers Guide to Paris
Bistro Cooking

Both by Patricia Wells. A couple years old so a few places might have closed but I find her to be great on restaurant recommendations from a little bistro owned by two sisters near the Eiffel Tower that was about $40 for dinner for 2 with wine to the real expensive place. Used her suggestions for nearly 10 years and been pleased.

Hang out as much as possible in the area around Rue de St. Germaine from about the church (St. Germaine) diagonally over to Notre Dame.

Check out a "little museum" the Museum of the Middle Ages. It is in an old monestary (convent maybe) and was also built on top of Roman baths which are in the basement. It houses a fantastic tapestry, "The Lady and the Unicorn".

For a not too expensive splurge meal try the lunch special (at least they used to have it) at Pierre Gagnaire. It is fantastic and last time I had it about $70 per person. This at a place where a friend buying me lunch onn another occassion insisted on buying the full course lunch for the two of us instead of the special. The full course topped out at a shade over 1000 Euros (not including the 300 Euros in cigars and cognac after lunch that I paid for). A problem with being drunk and having credit cards I suppose. But in any case, the lunch special is a huge deal if they still have it.

For an expensive splurge meal, Taillevent for lunch (cheaper) or dinner. Spectacular doesnt describe it adequately. Alternately the full service at Pierre Gagnaire.

We have also really enjoyed some of the wine bars around Paris. There is a chain whose name I forget. But they have a nice selection of wines by the glass and appetizer like foods. Good place to hang out and rest a bit. One is quite near Notre Dame, on the Left Bank on the street along the river.

If you like oysters there are some fantastic places for them in Paris. Have them with sausages.

Some "tourist" places are too good to avoid in my opinion. Les Deux Magot and Cafe de Flore are among them. Definately something to do at least once, although I find myself going back.

Check out the fruits and other food for sale at Fauchon. Also near there are 1 or 2 incredible chocolate stores. Maybe locals can fill in the names (Maison du Chocolate perhaps?).

Have tea at Mariage Frere. Beats English tea hands down in my opinion.