New Orleans will be hot, but I think that you can get away with doing it on the cheap.
There are great places to eat that will break the bank, but there are places to eat that are amazing and reasonable. And if you are into pretty much any type of music, you will be able to find clubs playing it. Most locals would say at night to avoid Bourbon Street and go to Frenchman street to hear music--but that might be a bit of a long walk at night back to your hotel.
Look in the thread SkyDog recently started to see some eating recommendations. Po-boys are a good cheap option.
I would note that a great date is to go to Cafe Adelaide for lunch and eat good food while each getting three 25c martinis. Then, walk along the river or in the quarter while you work off your buzz.
Also, if you want to go to Jacque-Imo's uptown, you can take the streetcar down to it and get to see the city that way. It isn't a far walk to the restaurant from the streetcar tracks. There tends to be a wait a J's, but you can try to hit it on a non busy night and there is a bar right next door to it.
On your way back, you could maybe stop by the Columns hotel for a drink. That's a fancy uptown bar/hotel in a nice area.
Also, this might help you:
Index To Over 300 Restaurant Reviews From The New Orleans Menu. You will have to do a bit of research to find the prices, though.
Oh, and I would not bother with a car rental. Just get a hotel downtown and take a cab or shuttle to it.
Just use Orbitz to find a good price on a hotel.