For the architecture you can do a self guided walking tour of the Garden District, there is also a cemetery out there too that you can tour as well. Either find an app or print off map with instructions off the area, and ride a street car out there to get started. The homes of Trent Reznor, Sandra Bullock, and the house where Peyton and Eli Manningn grew up are all out there and you will appreciate everything from the yards and fences to the homes and history.
Stop by Pat O Brien’s for for a Hurricane, it’s a pretty cool bar. You can also check out the Carousel Bar and enjoy a Sazarac while rotating around. Mothers Restaurant on Poydras
https://mothersrestaurant.net/menus/ for a Po Boy and the Acme Oyster House on Iberville for Chargrilled Oysters, a seafood platter and add on a soft shell crab. You can also try ‘gator there as well. Oh and get a Mufelata at Central Grocery which is out by the French Market. The market itself is pretty lame though, any meat (pepperoni) stick labeled as gator is 5-10% gator with the balance being beef or pork, disappointing.
Beignets and coffe at Cafe du Monde. Just don’t wear black pants, you’ll thank me later. Sucre for Macroons and while you are there, pick up an entire King Cake to take back to your room one night and just indulge yourself.