I recommend the following places to eat:
Camellia Grill (On St. Charles and Carrollton at the Riverbend) - open pretty late most nights, but I don't know its hours any more. It's relatively cheap and a can't miss.
Gulfstream (On St. Charles) - great for dinner, mostly seafood, could run you about $55 for two.
Frankie and Johnny's (On Tchoupitoulas St and Arabella St) - good neighborhood hang out with po-boys, seafood, and general American/Cajun cuisines. About $30 for two (good choice for cheap dinner).
Domilise's Po-Boys (On Annunciation and Bellecastle) - the world's best po-boys, hands down. Great lunch location, will definitely have a line. Call ahead to place an order for pick up - they've got all the big types of po-boys. They'll run you close to $25 for two, especially if you get two large po-boys.
Commander's Palace (On Washington Ave and Coliseum) - a must-visit! Plan on making reservations ahead of time and be prepared to wear a jacket to dinner. This place is 4 stars and is an absolute dining joy. Has won like the last forty billion James Beard awards for service in the Southeast. Dinner here can run up to $100 for two, but I believe it's honestly worth it. (Full disclosure: I used to work here and adore it as place of work as well as a place to eat)
Palace Cafe (On Canal and Chartres St) - great lunch/brunch location, another of the Brennan's family of restaurants (like Commander's). This is an upscale business lunch/dinner type place, splitting the difference between downtown and the Quarter. For lunch, it can run up to $50 for two.
Let me know if you'd like more recommendations, I'd be happy to make some more for eating. (There's obviously like Antoine's, Galatoire's, Red Fish Grill, Dickie Brennan's Steakhouse, Acme Oyster House, and the other choices actually in the Quarter - many of these are great, but parking is impossible, so unless you're already down there, they're inaccessible.)
As far as what to do during the day, like I said earlier, there are the Haunted Walking Tours at night, which are pretty cool. The Katrina bus tours are really interesting, as are the walking tours of the Garden District. Audubon Park has a really great, really cheap golf course, if you're a golfer. If you're downtown, our Aquarium is really pretty baller.