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Lots of good suggestions - I would add:
If Congress is in session you should hit Capitol Grill on a Tuesday or Wednesday to watch "Republicans Gone Wild!" (At least have a couple of Martinis at the bar . . .its the best show in town! )
Also:
The Source
Bistro Bis
The Monocle
Cafe Milano
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A couple of places to check out would be J&G Steakhouse (the steak is excellent, but so are the other items on the menu, especially seafood), Vidalia (excellent gourmet Southern cuisine), Acadiana (delicious Cajun/New Orleans food), and Equinox (local, seasonal cuisine. The President and First Lady dine here often!).
None of these places are necessarily cheap but they are all excellent.