prytania street area/lower garden district???
I think your hotel's at Prytania and Terpischore. By the time you get here, Cafe Reconcile ought to be reopened. It is three or four blocks on the other side of Saint Charles - pretty good versions of New Orleans standards served and prepared by high risk youth training for the food industry. As a note, that side of Saint Charles is a relatively high crime area, but I'd have no problem walking to and from Cafe Reconcile during daylight hours. You'll also pass on St Charles the Avenue Pub which has the city's best beer selection.
Heading the other way on Terpischore, walk through Coliseum Square Park and you'll hit Magazine Street and Surrey's Juice Bar, which for my money is much better for breakfast than the even more convenient to you Blue Plate.
Continue up Magazine, you'll find a couple of coffee shops, two Vietnamese restaurants (based in my limited experience both pretty good and fairly similar to each other), and a bit farther on Stein's Deli which is great but you may not have come to New Orleans for deli food.
After a fairly short residential stretch of Magazine, you'll see Tracey's a poboy shop/ sports bar. A block farther along that side street is Parasols a poboy shop/dive bar. Both specialize in roast beef poboys and a quick search will give you more information about the relationship between the two than you could ever need.
Soon enough you'll see, as someone else has pointed out, Coquette which is great. A little farther on is Joey K's a very friendly and solid neighborhood restaurant. The patio at the Bulldog bar is a pleasant place for a beer in good weather.
Your hotel is also within easy walking distance of the Warehouse District and the CBD with places like Cochon, Cochon Butcher, Domenica, and Luke, all of which have been extensively discussed on this board. The Domenica happy hour is a really good deal, though the restaurant isn't what I think of as low key.
Hope this is helpful and hope you enjoy your trip.