Naples with my 8 year old daughter.

Suspect Naples will be very hot. Perhaps the Bourbon Tunnel tour. Or maybe a funicular ride up to the Vomero neighborhood which is less crowded and has some great views. Be sure to get a lemon granita!

Regardless of your religious beliefs, you and your daughter might enjoy seeing shops in Naples that are world famous for creating and selling what in my family are called "nativity scenes" and sometimes called "creches" "manger scenes" or in Italian "presepe" : statues that recreate the story of Jesus being born in a stable including statues of Mary, Joseph, the baby Jesus in a cradle, along with barn animals as companions. Apparently in Naples, this is taken to a high art form and all sorts of characters are carved so that they too can be part of the scene...statues of bakers, fishermen, house painters, bus drivers, nurses, and just about anyone else you can think of (including celebrities). The stores are on the following street: "via San Gregorio Armeno. It is located in the centro storico, or historic district of Napoli, this street has hundreds of shops featuring hand-made presepi." I have not yet seen it but I plan to do so during our upcoming trip. I'm sure some of it is tacky, some impressive, but it is something Naples has been known for hundreds of years and I would think your daughter will remember it for many years!

More info:
https://www.lagazzettaitaliana.com/history-culture/7741-the-presepe-tradition-of-naples-italy
https://www.tripadvisor.com/ShowUserReviews-g187785-d195422-r418055023-Via_San_Gregorio_Armeno-Naples_Province_of_Naples_Campania.html

I like the idea of going to see the nativity scene shops, but being traditional shops in a traditional city I doubt many of them will be open in August. Especially if adaigaudioso will be in Naples close to the 15th.
If you decide to give It a try, once back home you could tell us if I'm right. Of course I hope I'm wrong.

Note that there are 2 underground tours of Naples. Both are quite interesting, there are videos on YouTube.

Naples Metro. Toledo stop is the most famous and is always listed among the "10 most beautiful metro stations in the world..." for a reason: https://www.google.it/search?q=toledo+napoli&client=ms-android-huawei&prmd=minv&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiKndSLyMHcAhUGZ8AKHR0tAMsQ_AUIEigC&biw=360&bih=511
But there are other Art stations where you could make a short stop while going around Naples: https://en.m.wikipedia.org/wiki/Art_Stations_of_the_Naples_Metro

The all city will be less crowded and even dirtier than usual.

We have seen those Nativity Scene shops and they are fun. Not only cribs and mangers, but whole suites of furniture for dolls houses. Think kitchen sinks and Steinway baby Grand Pianos. Really worth a look, and not expensive.

We were in Naples in July a couple years ago and went on an underground tour in the afternoon to escape the heat. It was interesting too!! Afterwards we wandered around the streets where the nativity scenes are sold . Beware that Naples is not well air conditioned. I was surprised that even the archeological museum was not.

There are some places to swim that a friend of mine took me to that would be refreshing too, although I do not remember where they were.

The heat will be the main challenge.

Beth