There are many different types of culinary venues available: from diners, to theme-based establishments, to the most formal dining. The College of Culinary Arts and Johnson and Wales University (http://culinary.jwu.edu/) provide a steady stream of well-trained chefs to the area.
Providence's Federal Hill district lives up to its heritage with some outstanding Italian restaurants, but there is great Italian cuisine throughout the state. If you happen to be in the area on St. Joseph's Day March 19th, pop into an Italian bakery and join the locals eating zeppoli, a heavenly sort of cream puff.
Unique Clam Cuisine can be found at "clam shacks" along RI's beaches, especially in South County. Chowder sometimes pronounced and spelled "chowda," in deference to the local dialect, is much debated and always delicious. The three major varieties are: traditional white made with cream, Manhattan red made with tomatoes, and Rhode Island clear unsullied by either cream or tomatoes. Add quahogs stuffed clams or "stuffies", clam cakes fried dough with pieces of clam in it, and a summer beer to guarantee a perfect trip to the shore, no matter what the weather.
The Port of Galilee is where many locals purchase live lobsters directly off the fishing boats to cook boiled with corn, potatoes, and quahogs at home.
Coffee milk is the official drink of RI and can be ordered in most local restaurants. It is sweet like chocolate milk and very nearly tastes like coffee.
Del's Lemonade (http://dels.com) is a state-wide phenomenon. Once delivered only in small "ice cream truck" style vehicles, it is now available in more than twenty-five fixed locations and in six flavors besides the original lemon. Get some.