We always go to the Bon Maison Guest House. It is on the residential end of Bourbon and is within walking distance to everything you would want to do.
The courtyard is so beautiful; we love sitting by the fountain in the garden. The rooms are furnished with beautiful antiques. Every room has a kitchenette, so it's easy to have fresh fruit on hand, or heat up leftovers. It has the best prices in the Quarter to top it all off!