Begin your New Orleans tour at 9am to explore some of the lesser-known neighborhoods of the city. See Lake Pontchartrain, Bayou St. John, the Faubourg Marigny area, Carollton, City Park, Faubourg St. John, the University Section, the lovely Audobon Park, the 17th Street Canal, and the Garden District. Visit one of the city's famous cemeteries, St. Louis Cemetery #3, to see one of the 'cities of the dead.'
Head out of the city to Destrehan Plantation at about 12pm, with a stop for lunch along the way. Note that while your entry fee to the plantation is included in the price of the tour, food and drink at the lunch stop is not.
Return to New Orleans in the evening. The actual return time will depend on traffic, weather, and possibly festivals or other events, so it's a good idea to not have any commitments that evening before 7pm.