Sorry it took so long to reply. I remember that you said in your email that you're leaving on the 28th (that's tomorrow!) I hope that you catch this before your flight and that you find these few notes helpful.
Oaxaca is one of the greatest food cities in Mexico. There is just simply an astounding number of places to enjoy sublime cooking. Even if I had the time, I could not possibly list them all. I'll try to list a few interesting places that I think would be convenient for you to get to from the hotel that you told me you will be staying at.
There are two famous markets in the city, the Central de Abastos near the 2nd class bus station and the Mercado Juarez/20 de Noviembre, just a block south of the zocalo. All the guidebooks list only these two and neglect to add that there are several other tiny neighborhood markets, many of which hide a few gems of their own.
One of my favorites among the smaller markets is just up the street from Hotel Golondrinas. The market is called Sanchez Pascuas and is about 3 or at most 4 blocks north on Tinoco y Palacios. The main entrance is actually on Porfirio Diaz but I am very sure that there is a back door on Tinoco Palacios. This is a really mellow place and never very crowded as the stalls are widely-spaced. In Oaxaca, I usually stay at a hostel on Cosijopi and so I consider this MY own personal neighborhood market.
There is a handful of fondas (food-stalls) on the T y P side of this market and a couple of excellent bakers towards the front. But the jewel of this market is the stall that offers quesadillas/empanadas. It's really nothing more than a couple of tables/benches and a comal set against a wall (the first dividing wall on the right if you come in from T y P). Try to sit right in front of the comal so that you can watch the senora pat out your tortillas and griddle-bake them on the lime(cal)-seasoned/lime(cal)-whitened comal. In the meantime, the other senora will probably be trimming the squash blossoms and getting the quesillo and epazote ready for your quesadilla de flor de calabaza. Since we have discussed and argued this little detail at length on the Chicago board, note that only the trimmed petal (the yellow part) and not one bit of green (calyx, stem, pistil) is used here. This is one of the finest quesadillas de f de c I have tried anywhere but make sure to try their other quesadillas as well (specially the empanada de mole amarillo). There is an excellent vendor of tamales sitting right next to them with a wide assortment of typical Oaxacan tamales, including tamales de chepil (we've discussed this herb on our board). If I remember correctly, the list of tamales is actually painted right behind them on the wall.
This is arguably the most glorious of Oaxaca's many street food forms. It's unique, it's delicious, it's beloved by all and could be found everywhere. Yet strangely enough, I have never seen a reference to it in any guidebook or food-listing for this city. Could all these gringo-tourists possibly be so stubborn about insisting on eating only their stupid resort-style fish tacos and California burritos and their fajitas that they could actually miss this splendor right in front of their eyes? I'm not going to describe it again as we've discussed this extensively on our board. The tlayuda itself (a thin masa "wafer" or disc, about a foot in diameter) could be bought from ladies sitting on the floor near the entrances of Mercado Juarez and crying "blandas, tlayudas". These blandas ("the" tortilla of Oaxaca) and tlayudas are still made painstakingly, in the traditional manner (metate etc) and only from the purest strains of corn. Several places around the market offer the "tlayuda preparada". That is, they turn those tortilla-discs (which look intriguingly a little bit like Mario Batali's Sardinian carta da musica) into the famous snack. They start by smearing one side of the tlayuda with asiento (see Chicago board) and black bean paste and stuffing it with queso natural and a choice of tasajo (air-dried beef) or cecina (in Oaxaca, cecina is always pork). The tlayuda is then crisped over coals on a small grill before being folded over like a quesadilla. During fiestas, dozens of vendors of this specialty will set up make-shift shops in the main plazas and in front of churches.
A personal favorite of mine for tlayudas is a rather evocative place open only from 8 to 12 at night. The address is:
Tlayuderia Las Reliquias
This is very close to your hotel (Morelos is 2 or 3 blocks to the south). It's on the south side of the street, east of La Soledad and within a block of the corner of T y P and Morelos. You might consider a tlayuda here as a possible late-night snack. This tlayuderia is actually a little atypical bec it is set-up (as a kind of side business) in someone's private house. You enter through an old wooden gate, cross a beautiful courtyard and head for the corner of the patio where the entire extended family encompassing several generations is sitting glued to the latest episode of some soap opera on the small TV. Someone will offer you the choice of the excellent tasajo or the cecina marinated in guajillo, fan the coals and make you your delicious tlayudas, all the while keeping one eye on the drama. There are a couple of tables and plastic chairs in the middle of the courtyard where you can enjoy your food right under the stars.
Alternatively, you could make this your dinner and then head a few blocks west to the nieverias in front of La Soledad church for dessert. The ice creams here are renowned and are still frozen and churned in the old way. You can see the garrapineras/barriles (holding salted ice) all in a row on the counters. Most of these vendors offer up to 3 dozen (!) different flavors including (in season) such tropical fruits as zapote negro, chicozapote, mamey, as well as "rose petal" (from the rosa de castilla). Note that they start from fresh fruits/flowers and do not use purees, preservatives etc. When I was last in Oaxaca in January, these places started closing down by 8 and I am not really sure when they start keeping late (summer) hours again. There is an excellent bookstore + cafe + internet cafe at the corner of the lower part of the plaza but they were also closing down by 8 in January. La Soledad is one of the greatest of Mexican churches and is home of the patroness of the city (la Virgen de la Soledad). It should (along with Santo Domingo church) definitely be in any visitor's itinerary of the city. The part of the La Soledad plaza that is elevated (going up towards Morelos) is called Plaza de las Danzas. At night, there are usually (traditional) dance or theater troupes practicing out in the open. Sit and people-watch on the steps of the plaza while enjoying your "nieves" as an unforgettable way to end your day.
I am going to make some tea and will be right back.