Check around the New Orleans Yacht club, and the Southern Yacht club. NOYC hosts Wednesday night races (during daylight savings time I recall) and the Southern hosts Friday night races. Generally willing crew are in demand and can get a ride. These are fairly casual races, but racing is one of the quickest schools in how to master basic sailing.
If you can get on the email list of some of the standard fleets looking for crew, you should get lots of offers of rides. Then it's up to you to try to get a second offer.
Don't know if this fits your definition of "sailing partner", but it's a good way to get started. I know daylight savings is a ways off, you might try just asking around the NOYC now. They're more of a public yacht club, while Southern is for members and those who are invited, but in general all of them are looking for decent crews.
Also the SYC offers adult ed classes in the spring, you need to make friends with a club member to apply but that usually isn't difficult. these I think are on Saturdays, in Flying Scots, if you're a novice you'd learn a lot and the cost isn't bad at all. Lessons in the summer too, on Tues and thurs evenings. These are kind of based on racing, since they would like to develop crews, but if you learn racing, you've learned sailing.
Full disclosure: I've occasionally taught in the SYC courses, usually the summer evening ones. They're a nice end to a summer day if you've been working in an office.
Last edited by nolatom; 01-19-2009 at 12:43 PM.