There are suggestions for Providence and the surrounding area in another topic: http://www.roadfood.com/Forums/topic.asp?TOPIC_ID=835.
You might find some ideas there – most of the places listed are good for lunch, though check on their hours. There’s definitely a lot of roadfood type places to be found here and that topic will point you to some.
As for other suggestions, I’d first want to know what type of food or experience you are looking for and in what sort of price range.
Al Forno is certainly a great restaurant, though many (including myself) think they’ve slipped a little; but the wait can be excessive and service sometimes poor and they are not open for lunch.