First, a word of caution. Many of these restaurants serve local beers, and several of these beers are good. The menus typically do not show the prices. My experience that $7.50 is the going rate for a craft beer in the French Quarter. Too high? The customer can decide when the information is available.
A second cautionary note: I've been here four days. I've mostly stayed away from Bourbon St. There are doubtless many fine establishments that I have not visited.
Highly Recommended
Cafe Beignet, 334-B Royal Street
Note: they also have a location on Bourbon St, which I never visited.
I ate breakfast here twice, and stopped in one afternoon for my obligatory beignet. Each breakfast I had the western omelette. This consists of a very good western omelette, grits, and two slices of french bread with butter. I had never before had grits, and they were fine, a good addition to the breakfast.
Cafe Pontalba, 546 Saint Peter Street
This is a great location, and I tend to be suspicious of restaurants with great locations. It's across the street from Jackson Square, diagonally across from el Cabildo.
It was pretty quiet when I went in, with a couple people at the bar and four police officers at one table. My waiter may have been the manager or owner; he reminded me greatly of Ed from E.Joseph and the Phantom Heart (https://twitter.com/ejosephmusic). The food was good. I had the pasta jambalaya and enjoyed it. I had an Abita Amber, or three, which I had tried a couple nights before at the Chartres House Cafe. The waiter was attentive and friendly and I was happy there, and left happy. Stepping out of the restaurant and seeing Jackson Square, the Cabildo, the cathedral, and so forth is an experience not available in Baltimore, not by a long shot. Like I said, great location.
Recommended
Chartres House Cafe, 601 Chartres St
Despite their web page, this restaurant is competent with a very good selection of local beers. I had dinner there twice. The first time I had their Taste of New Orleans. It had jambalaya, chicken andouille sausage gumbo, and crawfish etouffee. Very good. The waiter was excellent: he noticed right away when he made a beer suggestion (an IPA or wheat beer--yuck) and I immediately took something else, and then for my second beer he didn't make a suggestion. He was attentive, friendly, and did a great job. For reference, he was young, dark hair, thick dark mustache.
On my second visit, I got a different waiter, young and foppish, and I felt more like I was an obligation of his and less like he enjoyed his job. The beer I had was an English brown ale, the Southern Pecan from Lazy Magnolia Brewing Company in, get this, Kiln, MS. That beer was specifically the reason I went back: I wanted to try that beer; also I'd eaten at Jimmy Buffett's Margaritaville the night before, and didn't want another crappy dinner.
And dinner was fine. But with this second waiter, after the first beer and the main course, no second beer, no desert, etc., I was ready to go. He'd satisfied his obligation, and so had I. I should say the the maitre d' recognized me when I appeared, and was very welcoming.
Not Recommended
Tequila Blues Mexicajun Catina[sic], 1200 Decatur St
Okay, Mexicajun? I couldn't resist, and, besides, I needed lunch. However, had I walked another block or two SE, I would have been at the French market, and had no problem finding a better place. But maybe not something more interesting-sounding.
I had a shrimp meal with some green sauce on it. The side of grilled squash was good, but the shrimp was mediocre on first bite, and then many, many bites of mediocre sameness. Oh well. I've eaten at a Mexicajun restaurant.
Jimmy Buffett's Margaritaville, 1104 Decatur St
I ate at the bar, and had a pair of slightly different frozen concoctions, neither of which was remotely special. The meal had started to cool by the time I got it, or maybe it didn't come out of the microwave hot. There was a singer/guitarist who was good. Sitting at the bar was possibly a mistake since my back was to him, and I would have enjoyed the show more had I seen it.