The two above-noted places are not in the Quarter, they are in the Faubourg Marigny, on the North side of Esplanade. Street crime on the north edge of the Quarter has been increasing lately, so I'd be wary of staying up there if you planning on a lot of walking at night.
If you will have a car with you, that will complicate matters, as many of the smaller properties don't have parking arrangements for their guests, so you will also need to factor in the price of putting the car in a garage while you are there. If that is an issue for you, I recommend considering Le Richelieu; it is one of a very few hotels in the Quarter that has in/out onsite parking for guests. (There is a fee, but it's lower than offsite, as it is self-parking.)
If you want funky, try the Villa Convento; the top floor rooms are HUGE, and it is directly across from the Croissant d'Or bakery, and near the French Market. The elevator is TINY, though, so I don't recommend it if stairs are a problem. (Note that VC doesn't allow kids under age 12).
Note that the older small hotels in the Quarter are REALLY old; most are converted homes that date from about 1760. This means that it is generally not possible to get them as spotlessly clean as a modern room that has sheetrock walls and plumb floors. There will be a bit of wear and tear in the older buildings, and some mold is pretty much inevitable in the climate as well. Also, if you choose a place with a courtyard, the odds are that you WILL see large roaches on the ground in the evening; they are the same as Florida's palmetto bugs; they live under in the bushes and are pretty much impossible to exterminate entirely. Just thought I'd warn you about that, because some visitors are put off by it.
You didn't say when you are going, but if it is between now and the days after Xmas (but NOT the NY weekend), make it a point to check the Papa Noel rates; those are the best prices available all year.
https://holiday.neworleansonline.com/