I stayed at 70 rue Saint-Dominique in 2011 (a block closer to Tour Eiffel) and a google streetview tour shows many of the same shops nearby. Very easy access to Rue Cler as mentioned above.

IMO, rue Cler has become an overly touristified spot, a victim of the "Rick Steves effect," would not base hotel selection on location near it

But locating across the street from Thoumieux, a classic brasserie, is a good choice. Wander towards Fontaine de Mars and up rue Malar to l’Ami Jean and see what you think of their menus, too.

You’re right about Rue Cler being a bit too touristy. I only mentioned Cler Hotel because it has excellent reviews and it’s the hotel I would have personally chosen, or other highly rated ones in the same neighborhood, if I were visiting Paris as a tourist.
The area is quiet overall, yet it has lively streets like Rue Cler and a few others nearby, magical spots you can easily explore on foot. It’s also very well connected, with the RER C and Metro line 8 close by. What more could you ask for when visiting Paris?

You should reserve at Chez l'Ami Jean. Totally casual vibe but not cheap. Looking at a menu in the window won't really clue you in to what it's like to eat there. You can look at the menu on their website, just so you are not scandalized by the prices..

https://lamijean.fr/menu/

Since they can't walk long distances, keep in mind that as Seamus mentioned, there can be lots of stairs in the Metro. In addition, if you have to make a connection, there can be LONG walks in between, sometimes with up and down stairs along the way! Bus can be a better option.

Hi, I lived and studied in Paris for a long time before moving to Lyon, and I still go back frequently for work. Even though my roots and my home are in the Southern Alps, I know the city very well.

These days, when I’m in town for business, I usually stay at Relais Madeleine or Relais Montmartre.
They are under the same management and offer a great experience. Both are 4-star hotels, but depending on the season, they can be quite affordable and might fit your budget.
Relais Madeleine is very central, close to the Grands Magasins and Place de la Concorde.
Relais Montmartre is in the heart of Montmartre, tucked away just behind the Moulin Rouge. By the way, there is an awesome biscuiterie right across the street!

Both hotels are just a few minutes' walk from the metro. From my experience, the staff is professional and very welcoming. The rooms can feel a bit small sometimes, but that’s just Paris. They are definitely worth a look.