Running in New Orleans proper is limited by poor sidewalks, unfriendly neighborhoods, and a lack of greenbelts and trails. The best place to run will be the median (neutral ground) of St. Charles Avenue from the French Quarter to Audubon Park, and then to do a loop of the jogging trail inside Audobon Park, and then back, for about a 15 mile round trip. You can always cut this short by jumping on a street car. You will have to watch for street cars on your run down St. Charles, so run facing the street cars coming towards you.
The Rock and Roll group took over the Mardi Gras marathon, usually held in February. The first Rock and Roll New Orleans marathon was a success, with more participants - 13,000 finishers of the half and full marathons.
Varsity Sports keeps an event schedule for New Orleans and Baton Rouge and the surrounding area here - http://www.calendarwiz.com/calendars/calendar.php?crd=varsityrunning&&&j...
Another calendar is available from the New Orleans Track Club - http://www.runnotc.org/races/other.html
The Crescent City Classic 10K is New Orleans' signature 10K event. Held in the spring, the Crescent City Classic is flat and fast.
The Rock and Roll New Orleans Marathon is flat and fast, and should have good weather. New Orleans puts on a great party for its marathon, and any friends or family you bring as spectators will have plenty to do in the French Quarter.
On the north shore of Lake Pontchartrain, the Louisiana Half Marathon will go through the Tammany Trace, Lakeshore Drive, and downtown Mandeville.