Tourism is the number 1 industry in New Orleans so in spring and fall, you better book a hotel in advance. Especially for the big events such as Mardi Gras, Jazz Fest, Essence Fest, French Quarter Fest, Southern Decadence, Halloween, and Sugar Bowl you really should book a room at a very early stage.
Also keep in mind that for these big events rates are going to jump (doubling is not exceptional), and most hotels require a minimum stay of 4 nights during those busy periods. If you don’t mind a bit of a chill and rain, December is a perfect time to visit New Orleans. It is just before the Sugar Bowl and New Year’s activities, and hotel prices will fall considerably and big money saving deals can be found everywhere.
There are no very cheap hotels in the French Quarter, but you still can find a few places that offer quality accommodation at a reasonable price. If you’re on a budget and must stay in the Big Easy, give some thought to a guesthouse. Generally, however, you will find a better and cheaper choice of cheap accommodations outside the French Quarter.