For a first foray into La Villita, consider starting at the arched gateway on 26th around Kedzie and proceeding westward. East of there are certainly some good places, like the El Milagro cafeteria and store next door where you can purchase masa preparada or simply ground. I had need of a quick lunch in the area today and took some colleagues, who were all impressed with the offerings. They had both red and green chilaquiles, so I was happy.
Exploring in any direction is encouraged. Major north south streets and, especially Archer Ave., will have more large stores. North of 26th is one of the few places left in Chicago where you can see how retail establishments used to permeate the residential neighborhoods. Just in returning from El Milagro to California on the block north of 26th St., we passed corner furniture stores, fruterias, carnicerias, candy stores, lawyers offices, etc. This is a streetscape that has largely vanished in Chicago (due to zoning, etc.), and shows how much people in the neighborhood do business very locally.
If you are new to the South Side, notice also that there are both numbered Streets and Places. Places are one block south of the Street with the same number. I am not exactly sure where/how far south this starts, but it does exist at least in parts of La Villita.