I live in New Orleans, and ShanksE up there is incredibly sweet to reference the play I'm in.
You're way better off walking than driving-- aside from a necessary cab ride from the airport and back (assuming you're flying), a car is more of a pain than anything in NOLA because of the scarcity of parking. Unless you're really attached to driving or you plan to visit a far-off spot, it's a waste of money and time.
Jake probably means Oz, though the Pub is right across the street, and Napoleon's Itch is right across the other street, though there's usually not much going on there. The intersection of Bourbon and St. Anne is generally about as gay as it gets. And another block down Bourbon is Lafitte in Exile, another gay bar; a block up St. Anne is Good Friends, which is much more chill and laid-back than most of the gay bars with incredibly nice bartenders. Another block up is Rawhide, which is exactly what it sounds like. A few blocks west of there is the Corner Pocket, the gogo boy bar.
Gayness aside, the walk along the river is great and a good chance to get away for some quiet if you're ever in that mood. During the day, the street performers and artists are all out on Royal Street, so definitely save some time for the lower four streets of the Quarter when the sun is up.
Back to gayness-- the Marigny is our gayborhood, so hit up Frenchmen Street (not so gay, but great jazz clubs and local music of other kinds), Allways Lounge (burlesque and stuff), Kajun's (karaoke!), The Country Club (not what it sounds like; it's a bar/restaurant with a clothing-optional pool), John Paul's, and the Phoenix if you like bears.
Feel free to ask further if you want some non-gay, non-Quarter stuff.