All the plantation homes discussed are within easy driving distance of New Orleans. How many you can tour in a day will depend on your endurance (in the car and on your feet), how early you set out, how many of the same details you can stand to hear repeated, and how late you want to return (the small highways get a little intimidating after dark). You'll be driving through sugar cane fields and land ravaged by oil and chemical development. Don't expect to enjoy broad river views along the Great River Road (the roadway's name on both sides of the Mississippi); it's obscured by tall levees. But you'll pass through little towns that date from plantation days, and have the luxury of detouring to inspect them -- and take a chance on finding your favorite new road food.
If you have minimal time, we suggest viewing just Laura and Oak Alley; they are a mile apart, and each offers a different perspective on plantation life (Laura being classic understated Creole, while Tara-esque Oak Alley represents the showy Americans) and the tourism industry (Oak Alley is slick and glitzy, while Laura is more low-key but a superb presentation). Both are approximately an hour's drive from New Orleans.
If you're in New Orleans on Christmas Eve, consider driving along the River Road to see the huge bonfires residents build on the levees to light the way for the Christ child and Papa Noël (who rides in a sleigh drawn by -- what else? -- eight alligators!).
Some grand plantations were alongside bayous, which also provided water transportation. These are further away from New Orleans, and listed separately, with some lodging recommendations. There are also listings for lodgings in St. Francisville, which can serve as a convenient plantation-tour base.