The most prominent of the churches here is Santo Domingo, and if you are not religious you might want to skip the other 54. We paired that with a cab ride to Los Fuentes in one day, and walked back to the city after. Fonda de Santa Clara was a popular homely restaurant we tried and liked for the tri-coloured mole but we were not lucky with the other eateries especially around the Zocalo. Personally I did not appreciate the noise at the Zocalo and the dancing clowns that were the cause of it.
We took a local bus on the second day to Cholula (40 mins ride) to visit the great pyramid, despite mixed advice about local buses we found it to be simple and safe.
Although a UNESCO site, Puebla was not on my list of favourite places due to the rowdy evenings and lack of a cultural atmosphere despite the numerous churches. 2 days is more than enough, and the most important activity would be the trip to Cholula.