Markets and Resturants in and around Pueblo and Cuernavaca
You'll probably have better luck in Puebla, but here are some recommendations for Cuernavaca (where I spent 3 weeks in Jan. 2007)
La India Bonita
Marco Polor (Italian with mixed reviews)
Villa Bejar for their breakfast buffet
The dining room at the Tabachine golf course, also for the breakfast buffet (Tabachine is a gated community but the public is allowed in for the restaurant. It's worth if on a Sunday)
There is one central market in Cuernavaca. It's old, dirty and comparatively small, but definitely worth a trip. You'll find just about everything and anything you want. It's not huge and you can probably stroll the entire thing in less than an hour. Across the parking lot are some fondas that might be worth investigating. The woman I was with on this last trip wasn't interested in eating there so I had to pass. Also across the street from the main market is a block of fruit stalls. Fruit is dead ripe and delicious, prices very good. The market is perfectly safe but as with any place where you get a lot of people in a small space, pick pocketing is a problem. Don't carry a purse or back pack unless you absolutely have to. Use your pockets or a money belt. The folks I stayed use the mercado to purchase most of their meats and vegetables because it is "muy barato" (inexpensive). Quality is good and I suffered no ill effects from eating food purchased in the mercado. English not widely spoken at all in the mercado and not many non-locals.
Is this the cooking school you are referring to?
http://cocinarmexicano.com/ - is located in Tepotzlan which is very close to Cuernavaca. It's also pretty spendy, but I do know a couple people that have been participated in one of their programs and were satisfied.
Are you doing to language school in Cuernavaca as well? If so, which one? You will have a fabulous time, summer in Cuernavaca is busy but gorgeous. If you're doing language immerison, most of the larger school offer cooking classes on some afternoons. You can easily arrange these once you're actually there.
I was disappointed in Gaia, after hearing good reviews - the food didn't seem fresh or well prepared. La Madrigal and Las Mananitas were both really beautiful (with manicured gardens) and food was better than expected - service is beyond gracious. Both places, but especially Madrigal, are nice to see at sundown - you can go for just a cocktail and snack to see them.
In Tepozlan, Cirelo is really great, and the setting is pretty stunning (here it's the natural setting/mountains rather than manicured gardens). Two appetizers were favorites, and I would detour there for these: chalupas with goat cheese and the chilorio (spiced pork) taquitos. Worth it to go on a Sat. or Sun. to shop the market that takes over the central streets and have a meal at Cirelo (again, just before sundown to see the view).
In Tepoz, I finally learned the terminology for ice creams, and decided I much prefer "helado" (ice cream - like the Santa Clara brand) to "nieves" (ices), but they have an amazing array of nieves flavors available in Tepoz. Also tried pulque there, appropriately after the hike to the pyramid dedicated to the Pulque God, and it was pretty good - sort of lemonade-like.