I haven't read all the replies, but I definitely concur with the ones that recommend one of the historic inns (French Market Inn, Provincial, Place d'Armes, etc.). I would NOT stay at the Omni. There's absolutely nothing wrong with it, except that it's corporate. The historic places are part of very small local chains, and they do a much better job of retaining the NOLA feel. Why come here and then stay at a hotel that could be Anywhere USA? Ditto for staying on Canal or in the Warehouse District. It's fine, but more Anywhere USA.
Since you mentioned Frenchmen Street, my strong recommendation is actually the Lamothe House.
https://www.frenchquarterguesthouses.com/our-hotels/lamothe-house The front door opens onto Chartres Street (in the French Quarter), while the back gate opens onto Frenchmen. Sort of the best of both worlds. There's a main house with several rooms over a couple of floors and then a couple of other buildings set around the pool (all historic buildings, and at least the main house is haunted). Prices are reasonable, and the place is incredibly clean and nice. I had a friend who worked there until he retreated to New Hampshire during the pandemic, and it's always been my go-to whenever I wanted a staycation (I live a couple blocks from there).
As for activities, I think people have pretty well covered it. I'd just add that you need to take at least one walking tour from Haunted History. Whether you believe in ghosts/vampires/etc or not, they give extremely well researched historical tours that present the documented facts along with the supernatural allegations. I have a couple of friends who are tour guides with them, and their knowledge is encyclopedic.
Also, since you'll be in town for the holidays, take in at least one Reveillon Dinner.
https://holiday.neworleans.com/tradition/reveillon-dinners/ ears ago we only did Bourbon.The tradition dates back to the early 1800s, and it's now celebrated by some of our most revered historic restaurants (Antoine's, Arnaud's, etc). Carefully crafted and reasonably priced menus, and the chance to dine among the oldest NOLA families. If you choose Antoine's, be sure to ask for a tour of the restaurant...trust me on this
Any specific questions, just ask!