Paris food recommendations near our hotel in the 6th?

I would really recommend Polidor which is at 41 Rue Monsieur le Prince which is very close to where you are staying. Very small place but food is excellent and a great ambience

Polidor, 41 Rue M. le Prince, has been a favorite of ours (and of Rick Steves) -- recently started accepting credit cards.

Or if you like to wander around, cross Blvd. St. Michel and enter the maze of little cheap restaurants (€10-15-20 menus) between Blvd. St. Germain and the river -- no bonus points for telling your friends where you ate, but it can be fun.

This is great, keep it coming! We do love to walk and wonder, and will probably only use our feet whilst in Paris.

Among the 40 or so restaurants where I have dined in the 6th, these are my favorites:

Armani Ristorante
Quinsou
Wadja
Aux Prés
Toyo
Le Cherche Midi
Evi Evane

On the list for future visits:

Mercerie Mullot
Esttia

Wow @tocard sounds like I picked a good area! Thank you!

If you decide to eat at Polidor - watch Midnight in Paris before you go! Polidor features in that film!

https://en.wikipedia.org/wiki/Polidor

You could also eat closer to the Eiffel Tower. One of the googlemap walking routes takes you by La Terrasse at the corner of Avenue de la Motte-Piquet and Avenue Bosquet.

If you walk the route along Rue de Grenelle you'll also go past the Le Roussillon at the corner of Rue de Grenelle and Rue Cler plus any number of other restaurants. I also like the Italian restaurant Gusto Italia on Rue de Grenelle almost to Avenue de la Bourdonnais. There are 2 across the street from each other. I prefer the more restaurant-y one which would be on your left as opposed to the more carry-out one on the corner on the right. Food is good either place.

PS Watch Midnight in Paris anyway! I'm neither an Owen Wilson or Woody Allen fan and I love this film!

PPS I've walked from the Odeon area to the Rue Cler area many times and it's not a bad walk, depending on how tired/jet lagged you are. If you are tired, Metro Line 10 from Odeon stop will take you to the Motte-Picquet stop which is near the ET.

To the folks who suggested watching “Midnight in Paris” thank you so much. Incredible film, enjoyed so much!

I'm so happy you enjoyed it! Now you'll have to watch it again when you get back just for the scenery - Oh look we ate there, Oh look, we saw those steps, hahaha!

I just left Paris after a week and while there we returned to
La Bistrot D' Henri
16 Rue Princesse near St Sulpice
La Cuisine de Philippe
25 Rue Servandoni nearSt Sulpice
both in the 6th near your hotel.
Mike