Oberlin is one of the best examples of Providence's fantastic dining scene—expect a wide range of excellent lesser-known, sustainably caught local fish like tautog, butterfish and bluefish, as well as a wide range of other regionally-inspired dishes like fresh pasta, homemade sourdough, and roasted local veg. The place has a real neighborhood vibe that makes you want to stay for hours, which is definitely helped by the exceptional wine list and desserts (specifically: the Basque cheesecake).
A beautiful melding of old and new architecture, this museum houses a wonderful collection-Ancient Art ,18th & 19th century furniture, Impressionist paintings, textiles, plus rotating special exhibitions. And museum store is great, and full of products made by RISD (Museum of Art, Rhode Island School of Design) graduates.
Hungry Ghost is an artist-owned studio and shop that sells a range of merch (all printed in-house), as well as repurposed vintage apparel, patches, pins, local zines, VHS tapes, and other deadstock eccentricities. Great for souvenirs and niche Rhode Island joke products (like their notorious "Rhode Island Slut" sweatshirt, inspired by a scene in the original Dumb & Dumber movie).
Julian's is a Providence staple. It has amazing brunch, is vegan friendly, serves sweet treats like apple & spice cocktails & cherry cinnamon buns, and has a cozy-stars wars-cheerful-rock & roll vibe. I feel happy every time I go there.