I know New Orleans pretty well, DC a bit too. Beyond the obvious in DC (much of which is a lot of fun), I recommend a tour of the
State Department's diplomatic quarters. It's free but by way-advanced reservation only (check the link). It's like taking an elevator up in a plane ugly government building and landing in the Palace of Versailles. The tour guides are very good at making it interesting, too.
To me, DC's best restaurants at the medium-low end are the ethnic places. Grill From Ipanema (medium) in Adams Morgan serves tender Brazilian steaks and clay pot fish stews. Also in Adam's Morgan, Meskerem and Fasika's have great Ethiopian food (don't laugh, it's good). Jaleo's (medium-expensive, depending on lunch or dinner) is a good place for Spanish tapas. I like Thai food, and 4912 Thai and Kanlaya are both cheap and great. Bacchus serves Middle Eastern in Dupont Circle, I had an awesome goat curry with pine nuts and yogurt there. Bistro du Coin is not-quite-expensive, top French food (give me some duck) but casual atmosphere. At the high end, Galileo (Italian), 1789 (American), Kinkead's (seafood), and Makoto (Japanese) are some of my favorites.
In New Orleans, the best things to do are just walk in the French Quarter, down by the river and Jackson Square, also the Garden District. Be careful, some areas can be very spotty, stay out of graveyards, for example, unless you are ready for a gunfight. The D-Day museum is as good a war museum as it gets, right up there with anything in London.
I definitely know food in New Orleans (the best city I've found for it), having spent many weeks here on an expense account. Unfortunately, that means almost all the places I know are very expensive. Commander's Palace is ridiculous. Brennan's is the place to go for elaborate champagne breakfasts. Galatoire's right on Bourbon St. is a very old-school institution (coat required, no reservations allowed, great traditional dishes, loud, and sometimes rowdy). Dickie Brennan's has the best waiters and is my favorite steakhouse anywhere. Antoine's, Arnaud's, Gabrielle, Emeril's, and Palace Cafe all served memorable meals that made me go back.
Cheaper places: Liborio's is the best Cuban food I've had outside of Florida (go at lunch, same food, cheaper price). Mother's is renowned for it's po boys and turtle soup, has lines out the door on busy days, and is actually worth the wait. Crescent City Brewhouse has nice beer and huge portions of good food (sounds less appealing than it used to). Mr. B's is cheaper than the high end but still not cheap, has great food and is very relaxed.
Can you tell I used to eat a lot?
