You are right on the zocalo in the historic part of the city. There is a wonderful little museum, the bandstand, a pretty good breakfast. By Mexican standards, it is a bit expensive and can be noisy depending if anything is happening. Many people prefer the b&b's in Comala. 20 minutes from downtown. Look at other posts to get the names.
Since you are going that far, I would suggest a visit to Suichitan, eat a lunch under the coffee trees, at the only restaurant in the village. and ask for directions to Gorgonios house. He is an exquisite carver and in San Fran galleries, his work sells at 10x the price he will quote you. Do not bargain with him.
You will have a blast and if you are craving non Mexican food, I highly recommend Basta Pasta. There is also a great Oaxann restaurant in walking distance from your chosen hotel on cinque do mayo that is also really good.
Have fun