My wife and I are staying at the Chateau Frontenac and the museum is close.
Is it worth visiting??
Do you have any ideas for a nice quiet dinner near our hotel?
If you are interested in fashion and the dress styles and Dior, then Yes, it's absolutely worth visiting! For my wife, it was one of the highlights of our time there.
Get tickets in advance.
There is a Galerie Dior
https://www.galeriedior.com/en
and a hotel Château Frontenac in Paris
https://www.hfrontenac.com/en/
Dior museum in Paris? I'm not even a fashionista and I found it fascinating (also because I had just watched the Dior show on Netflix, The New Look, before my trip). The history is what gets me, not necessarily the 'fashion', ymmv.
The OP used the correct name. They’re staying at the hotel called Chateau Frontenac in Paris which is less than 5 minutes walk from the Galerie Dior. The Galerie Dior is the museum of the haute couture house of Dior.
I visited the Galerie Dior last summer during the Olympics when, amongst many other beautiful items, the dresses worn by Celine Dion, Lady Gaga and Aya Nakamura during the opening ceremony were on display. I’m not a big fashionista but I found the museum very interesting and enjoyable to visit.
Be aware though that the Galerie Dior is closed between May 5 and May 20. They will reopen on May 21 https://www.galeriedior.com/en