Awesome, I was just up there last weekend! Yes, I'm an RI boy like @dracisk. Oberlin is strong, but it will cost ya! Try the crudos. Jacques Pepin was there recently. Hemenways has been around forever. I've not been there in forever but it's solid. Sorry you can't get into Al Forno, but keep trying, it's worth it. The summer grilled pizza with local sweet corn is amazing. My brother has known George (RIP) and Joanne since their original location on Steeple Street! In fact, he visited with them at their summer place in Provence and they had lunch with a neighbor you might have heard of -- Patricia Wells (no relation).
Now back to RI food. Old Canteen and Camille's are old-style fancy shmancy spots. Angelo's is very casual. Worth checking them out for a taste of old RI. There are a ton of newer spots on the Hill you should investigate. Also up there is Caserta's, which along with Twin's in North Providence are exemplars of another style of RI-pizza, thicker, with a crunchy crush. At both places cheese is an optional topping and i recommend you just get mushrooms and olives at either place.
There's a new seafood shack in the Jewelry District (Dyer Street) called Dune Brothers -- great RI clamcakes, fish and chips, and lobster rolls. They have done so well they are already opening a bigger place on North Main Street.
Now, for some baked goods. Seven Stars is a great bakery on Hope St (with other locations), Scialo Bros on the Hill is a 100+ year old place on the Hill that closed earlier this year (the sisters who owned it are really old) and shut off their ovens, which are original (apparently turning them on is a big deal). Things looked bleak but a buyer was found, with the agreement that one of the sisters would run the place, and they got the ovens turned back on. I.E., this is unique place and worth a visit. LaSalle Bakery is another old-line italian place and there are many others. Also prevalent are Portuguese bakers, with huge loaves of sweet bread, custard tarts and other delights.
if you can get to Mikes at the VFW in Cranston, do so. Excellent homestyle italian food in an actual active VFW Hall. Cash only! Bonus: The locals are a trip. You'll likely see guys in colorful track suits, even in the summer. Try the polenta!
There are some great Latino places in Central Falls (hometown of Viola Davis) and even several african spots there, in Pawtucket, and the West side of Providence.
Chez Pascal is a wonderful french spot on Hope St on the East Side. There's a place across the street called Avenue N that looks really good. If you need more tips let me know!
PS on the way back I swung by Zuppardi's in West Haven for a clam pizza and it totally rocked. Their cannoli are great too -- massive and delish. Easy access from 95 -- just call from the car and the pizza will be ready. Nice alternative to the big-name spots, been in the same family since 1934!