OK. For starters, since they are only getting started now, they will have to narrow their dates to March 9-12. Mardi Gras is essentially sold out, and nearly every hotel near the Quarter, CBD, or Garden District will have a 5-night minimum running from the previous Friday through Tuesday night. They should plan to arrive no earlier than Wed, Mar 9th.
Ash Wednesday (March 9th) is deathly quiet in the Quarter. New Orleans takes that day pretty seriously, and lots of businesses are closed for a bit of a rest after the run up to Mardi Gras. However, the private museums and such are normally open, as is the State Museum (to the chagrin of nearly every state employee south of Alexandria, Ash Wednesday is not a State holiday.)
The best hotel bargain in the Quarter, bar none if you're driving, is Le Richelieu, because it has FREE onsite guest parking. (It is the only hotel in the Quarter that does.) I just checked, and for those dates they can get a queen bed for $135/nt, or a King for $145, not including taxes. They will not get breakfast, but there are several good breakfast joints in that part of the Quarter. For folks who like atmosphere, a little place that I like to recommend is the Villa Convento, especially the top floor rooms. It's little, a bit tatty, very funky, and the family who own it can be quirky, but those big attic rooms have a view over the Quarter to the river that will make you almost think you're in Paris.
HOWEVER, if this is all about eating, and they want trendier food (as opposed to New Orleans traditional cuisine) they might want to stay in the Warehouse District instead, because that is where most of the trendier restaurants are. Most of the hotels in the Warehouse District are chain properties located in ... yep, converted cotton and coffee warehouses. (There are not many good breakfast joints in the area, as it caters to conventioneers and people leaving on cruises. For good breakfast joints you have to venture a little bit north into the CBD and share breakfast with the poor slobs who toil in banks and law firms. Tourists always want to go to Mother's for the po-boys, but their breakfast is an institution.)
If they want to try Uptown in the Garden District, one of my favorites there is the Park View Guesthouse, which is adjacent to Audubon Park next to the Tulane Campus. It's high Victorian, and quite elegant, and you have the Park right there to play in. For less fancy, and in a more ordinary neighborhood, I've heard good things about the Chimes B&B in the Lower Garden District near Touro Infirmary. The Prytania Park is also very popular.
Now then, the restaurants. They should not have too much difficulty getting reservations at the end of that week; most locals are pretty partied out and will be eating out less for a while. Unless they have religious objections to pork, one of the must-do's will be
Cochon. It's not very expensive, but it's great; it's owned by Donald Link (see also
Herbsaint). If they like John Besh, he has several restaurants in the city, the two most popular are
August and
Domenica.
Bayona has been around a while, but it's still
very good, as is
Brigsten's. For lunch they really should try
Le Petite Grocery, and for sweets,
Sucre is indescribably yummy. For a local traditional favorite that will be an experience,
Mosca is truly unique (get GOOD directions and a map; it's out in the sticks and very nondescript on the outside. Inside it has James Beard awards.

Mosca is cash-only, btw; has been since it opened in 1946.)
For Zydeco, the best place in town is definitely Thursday Night at the Rock n' Bowl, uptown on Carrollton. Definitely a dive, and the cover is kind of high, but loads of fun and a unique local experience.
PS: Mother's is the restaurant that was described above by Cristy, it is in the CBD, on Poydras. I personally don't find the po-boys worth the wait at lunchtime; there are other places for po-boys that I like just as much.