Haven't been in years but back when I lived in Providence my friend from Mexico City loved the Pozole they had on weekends at Restaurant Mexico Garibaldi on Atwells. If you don't like it then Chilangos is just down the hill. I remember Lupita on Dexter St. in Central Falls being great too.

Providence area does fairly well with Mexican food from Mexico, but it does not do Tex Mex, just to adjust your expectations.