Food....yum!

You could start by browsing the website TheFork. Fill in their form with the neighborhood, the date, the type of food, etc., and it will list descriptions of restaurants open on the specified day. It is a very reliable service and is convenient if you want to make an on-line reservation. Some restaurants offer special discounts, but be sure to read the fine print about that.
http://www.thefork.com/city/paris/415144

Here's one of my favorite restos in the 5th - La Fontaine dela Mouffe, at the corner of Rue Mouffetard and Rue du Pot de Fer. Rue Mouffetard is just West of Rue Monge, so not far from you. The fondue is great - haven't tried other items. They are open on Sunday. Or my favorite steak/frite restaurant is near the St. Germain des Pres metro stop, if you've wandered that direction. It's called Le Relais de l'Entrecote and is at 20 rue St. Benoît, a small street near the St. Germain Church. They open at 7 for dinner, but get there at least 15 minutes early since a line forms. Steak is the only main dish (27 euro I think) but they have appetizers, wine, and dessert. They are also open on Sunday.

Although I haven't tried it yet, when Anthony Bourdain's No reservations was in Paris, they ate at Café Les Papillon (129 rue Mouffetard) and raved about it. I think it is very close to Place Monge. It's on my list to try on my next visit (hoping it will be soon!) If you google the show, you can watch it online.

Have fun!

We liked L'Epoque and Le Descartes, both on Rue Cardinal Lemoine at the corner of Rue Rollin, a short block north of the Place Contrescarpe (where there are several other places). This is a few blocks up Rue Lacepede from the Place Monge Metro. Don't know about Sunday opening though.

You're bound to find someplace good nearby, even if you have to ask your hotel clerk. It's hard to get a bad meal in Paris! Have a great trip.

Hi Susan... : ) ... if it were me, I would walk down to my favorite cafe at the western tip of Ile St. Louis called La Flore en l'Ile. Great food, great ambiance (especially if you sit outside) and great location. Be sure to check out the street entertainers right there on the pedestrian bridge... : )

Thanks to everyone for your help! These are all great ideas I will look into.

Check out Paris By Mouth . . . .they have a whole entry on places open on Sunday, divided up by arrondissement and whether you can just drop in or need to reserve in advance. They're a great restaurant resource in general (no I'm not affiliated with them).

P.s. good for you for thinking about this and making a plan ahead of time. Much better than the frustration and hunger pangs that would come from wandering out of your hotel on Sunday night and discovering to your chagrin that most places aren't open! This is what we talk about when we talk about the importance of planning and the return on investment. Because you are spending the time now to research your options, those 2-3hours Sunday night for your first night in Paris will be so much more enjoyable!!

Thank you Kim, I really do appreciate your kind words! That makes me feel very good in light of the fact that most of my (non travel) friends think I'm controlling and over planning. I certainly am to some degree, but more importantly, like you said, I'm planning for the return on investment. And, I think I just want to "live" in the trip as long as I can!

Don't let them get you down. It's your money and your time, both of which are important to spend wisely! They can "go casual" on their own trip!

Here's a recent article in the NY Times. Studies have shown that you get more happiness from planning the trip than the actual trip.

http://www.nytimes.com/2014/05/11/travel/what-a-great-trip-and-im-not-even-there-yet.html?emc=edit_tl_20140510&nl=travel&nlid=65909356&_r=0

I used ParisByMouth to find restaurants open on Sundays. It is very hard to find good restaurants on Sundays.

We went to La Rotande, 105 Bd du Montparasse, which was near our hotel. It was 50/50 tourist and French. They are known for their seafood. But I went for the standard touristy items of onion soup and snails. There is an English menu and the staff was friendly. You can check out their website. Continuous service, so you don't need to make a reservation.

You are near Rue Mouffetard. We walked from there along Blvd. de Port Royal to Blvd du Montparnasse. You could return going north and go through Luxembourg garden back to your hotel or vice versa. I think each way was about 45 mins leisurely walking.

chun-that's a fascinating article. I have re-posted it in General Europe for others.
Dave