Just a follow up to this thread so that others who may be searching for dining options in these places can benefit from my recent experiences as well as the great suggestions given above by other flyertalkers.
We liked:
Los Girasoles in Mexico City
Expect really imaginative food and delicious margaritas in a beautiful square with outdoor seating
Los Danzantes in Oaxaca
Great food-try the duck tacos and the goat cheese flan! We ate here twice we liked it so much.
La Biznaga in Oaxaca
Just as good as Los Danzantes and 1/3 less expensive
Also in Oaxaca: Pan bakery for good coffee and pastries at breakfast...and the pizza place next door was excellent too (both on the Garcia Vigil)
Mesones Sacrista Restaurant (courtyard of the hotel)
Try the mole sampler plate to get a taste of 4 different types at once
If you are looking for lodging in Oaxaca, I highly recommend Casa Catrina. It is ideally located, close to good restaurants and the zocalo. The rooms are very nice and the staff is wonderful.