I frequent Pauly Penta' s Mineral Springs Ave in North Providence (everything is good but it's $$$$) and Chi Chi's, Douglas Ave. (thinly layered eggplant to die for!). I've also heard the chicken salad is great. I usually land there mid afternoon and it's always sold out.
I'm a big fan of picking up prepared foods to bring home for dinner also. I travel all over MA and RI and have a penchant for Italian delis. I've been to Venda's Tony's on the hill. I'm always looking for new places to try.