Thanks to everyone for helping me by answering my questions and posting their opinions.
First night (and turned out, last night) was at a small local place (in the 6th) called Aux Saveurs de Claude (www.auxsaveursdeclaude.fr). Was actually recommended by someone on Fodors. If you love local, casual ("comme chez soi") food without any attitude and a lovely welcome, this place is for you. The kitchen is open so you can watch Claude and his assistant make you your dinner. There is one waiter who speaks English and is very warm and welcoming. The food is delicious- nothing fancy, no great gourmet dining, but wonderful nonetheless. The menu is small, but there is definitely enough choice. There are about 6 starters and 6 main courses. Everyone around us seemed to be starting with the lentil soup with fois gras, and as we don't eat it, we started with crayfish in quick puff pastry and snails on purple potatoes with garlic cream butter. The crayfish was just ok, but the snails were delicious. For dinner, we decided to split a main course as we were not that hungry, and it's good that we did as we split the cote de boeuf (basically, steak) in a delicious wine/pepper sauce. It was served with whipped potatoes and carrots. The kitchen split the order for us, and it was absolutely enough for the two of us. For dessert, we ordered one plate of "chocolate dream", which was a plate of homemade chocolate ice cream, chocolate pie, a glass filled with molten chocolate and one other item. It truly was a chocoate dream. I did not look at the wine list, but chose to drink a 1/2 bottle of champagne with my meal (I was travelling with my daughter, so I was basically "drinking alone"). As I mentioned, we were so happy with our meal and the whole experience, that we went back to the restaurant on the last night (and they welcomed up back so warmly!!). The second time we passed on the crayfish and ordered the snails and another dish, grilled endive with melted cheese (can't remember what type) that was delicious. We split the steak again, and I had a cheese course (simple, but way too much for one person)and the chocolate dream. We rolled out of there with kisses and hugs and promises to be back next year.
Second night was Sunday, and chose La Mediterranee at Place de l'Odeon. A little more, but not much, more formal than the previous evening. The restaurant's making a bit of a comeback, having had it's hayday in the 1950s-1960s. Jean Cocteau painted murals all around the restaurant and his artwork is shown throughout. Pictures of famous patrons such as Liz Taylor and Eddie Fisher and Queen Margaret are on the wall and make for interesting viewing. When we arrived, they showed us to a table in a glass-enclosed room with all the other Americans who were looking for an open Sunday night place. I immediately said no, and they said the only other place was a no smoking room, which was fine with me, and we moved to a much more comfortable and pretty room. The service was indifferent at first, and the waiter totally forgot to serve me the glass of wine I ordered with dinner (and then, of course, charged me for it on the bill). However, if you can get over that, the food is good. We shared a dozen oysters, presented properly with mignonette sauce, and they were pretty tasty. For dinner, my daughter had her first taste of dover sole, which she loved. I had the bouillabaisse and it was also delicious and correctly served. It was almost as good as anything I had in the south. In fact, my portion was so large, that I could not finish it (to the consternation of my waiter). We did not order dessert, but were quite satisfied with what we had. I don't know that I would ever go back there but if you like fish and a different kind of atmosphere and you can speak French (I do) you might pull off a good meal at a "reasonable" price. (for all our meals, the bill came out roughly to 100 euros a night).
The 3rd night was at Chez Josephine (Dumonet). I had read alot about this venerable bistro, and I was looking forward to our dinner there. Of course, they could not find our reservation that I made (this ALWAYS happens in Paris at least once a trip) but they had a table, next to the kitchen available. We took it (where were we going to go?)and it turned out to be fine as the chef kept coming out to talk to us and the kitchen staff kept waving to us while they were cooking. This restaurant is known for their truffle menu and 1/2 portions. They have a number of different preparations for the truffles, and you can order most of them in 1/2 portions so they are not ridiculously expensive. We ordered the sliced truffles on potatoes. I honestly have to say that we were dissapointed. The truffles truly had no flavor. I have to also say that I have had truffle dishes in NY this fall that also had no taste. Is there something going on with truffles this season?
For dinner, I ordered the steak tartare which came with thin slices of sauteed potatotes with garlic. The steak tartare was the best I ever had. My daughter had the 1/2 portion of boeuf bourginon which was HUGE and also the best I have ever tasted. For dessert, we shared the grand mariner souffle, which was beautiful, but just ok. This is a restaurant I would go back to - a mix of tourists and locals- just for the steak tartare.
Just want to also mention that one of the things we most enjoyed eating were chicken sandwiches on a large baguette made by a boulangerie on the corner of Rue de Rennes and Notres Dames de Champs!!