Get the chateaubriand and the profiteroles (then waddle back to your hotel). Speaking of, there's a great hotel in that area called de Varenne.
It's near both the Musée Rodin and d'Orsay, which are much better experiences than the Louvre even if they don't quite have as huge a collection (though d'Orsay is up there). Also you're near the Latin Quarter which has some of the best sidewalk cafes (though you won't want to eat for a while after Le Square).
If you want high-end dining (and are willing to pay for it) I cannot recommend highly enough l'Atalier du Joel Robuchon, in St. Germain des Pres.
Personally (people will violently disagree) I say stick with the Left Bank. The 5th, 6th, and 7th are the best parts of Paris at least for me, and you really can't fail to have a great day just walking around and seeing where the city takes you.
That said, if you do want to venture north of the river, Montmartre is always worth seeing. There's an amazing Moroccan place called I think Clare de Lune near Etienne Marcel (which is basically the southern edge of Montmartre), and a whole lot of other north African places inside Montmartre.
I hate to be one of those killjoy expats, but really most of the heavy-tourist stuff in Paris you can do without: the Eiffel Tower looks exactly the same in person as it does on a postcard, and you'll get a better aerial view of the city when your plane is landing. The Louvre and Notre Dame are amazing (and you should probably at least walk by Notre Dame) but the crowds are just hellish and, frankly, it makes you feel like you never left the US. Speak whatever French you have; as long as you make a good effort I've never found a Parisian to be rude about it (and I look Tunisian, which can be bad). I'm crazy jealous; have a great trip!
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