Suprisingly, there aren't a lot of B&Bs in the French Quarter - you would think there would be, but there aren't. There are plenty of B&Bs in other parts of the city.

Check out this list though - B&B Hotels, which are basically smaller hotels that also serve breakfast - might be what you are looking for:
http://www.neworleansbandbs.com/bed-and-breakfast-hotels.html

Thank you for this info..............what about B & B's in the Garden district or another district not so close to Bourbon St?

Stayed at Monrose Row, just outside the quarter. Cindy the owner is great. The home is perfect.

If you want to be near a lot of bars and restaurants and other sightseeing, the FQ is where I would stay, with the Faubourg Marigny as a second choice - staying close to Frenchman Street, which has a few block of cool bars, clubs, and restaurants too. Most of the FQ is not Bourbon Street or anything like Bourbon Street - in fact, only a few blocks of Bourbon Street is what people usually think off. Most hotels in the FQ are on fairly quiet blocks without a lot of partying.

You can stay in the Garden District, but that area is very quiet and residential - it would require a streetcar or a cab ride to get where you want to be. There are plenty of restaurants and things up town as well, but most will not be walking distance to your hotel because uptown isn't as compact as the FQ.

When I travel alone, I generally prefer to stay in the thick of things so that I can come out of my hotel and be where I want to be rather than reliant on taking taxis or even having to walk far.

If you stay in the GD, make sure you choose someplace on St. Charles or within a block of it so you can take the streetcar back at night without having to walk far from your stop. Since the GD is pretty quiet, you won't have a lot of foot traffic at night - or really most times of the day. In the FQ, people are pretty much always out and about, so you don't have to worry much about deserted streets.