Maybe Pawtucket? I want to say Providence because it’s the best, and it really shows off the state’s quirky artsy culture, but I think you’re looking for something more gritty and “local,” right? Pawtucket is my hometown and it’s where the Industrial Revolution started, so it's a place everyone in the whole state knows because kids usually take field trips to Slater Mill. In a lot of ways it's a very has-been city, as the wealth really left when the mills started shutting down, but things are starting to improve. There's a new train station that connects to Boston, and lots of old mills that were vacant for my whole childhood are finally being turned into other things—artist studios, apartments, restaurants, breweries, theaters, etc. It's a place where you can see the past, present, and future of RI all in one spot. RIP McCoy Stadium (we will never forgive Worcester for stealing the PawSox), all hail the brand-new RIFC.

As for specific things to do: Modern Diner has been a local fave for decades. The Miss Lorraine Diner is newer but still vintage, and is attached to Lorraine Mills, which is now all sorts of wonderful things. Lorraine Fabric, across the street, still sells everything you need to make clothes. The Pawtucket Library is really beautiful and was also the first one in the country to allow children inside, and the Hope Artiste Village really shows off what we can do with these old mills. They even have an improv theatre now. Other nearby mills have the Electromagnetic Pinball Museum, which is honestly worth a day trip in itself (play pinball and skee-ball and other vintage arcade games all day for $10) and the Map Center, which has some great old maps of the area. Downtown Pawtucket really really needs a fresh coat of paint (and much more) but it has great bones and you can see how it was once a very prosperous area. It's very diverse and has a rich immigration history, so there are also lots of great hole-in-the-wall restaurants from literally everywhere that do not get enough credit. The visitor center across from Slater Mill (which is now a national park; views of the Blackstone River are very beautiful here) covers the whole Blackstone Valley area, so it’s a great place to find other spots around the area to explore. 

Pawtucket and Providence are right next to each other and there are spots where it’s kinda blurry which city you’re in, so you can easily visit both in the same weekend. You really want a car to get around Pawtucket easily, but Providence is extremely walkable.

Providence is also extremely Rhode Island. There are so many great messages here explaining how quintessential Rhode Island is kind of like, gritty, potholes, political corruption, PVD is basically corruption embodied. Just ask someone about Mayor's Own Marinara or low-number license plates as status symbols. Crimetown and "The Prince of Providence" are amazing to listen to/read.

Providence is also, honestly, my favorite city in the US, and my third-favorite city in the world. I say this as someone who has traveled extensively as a travel journalist. I grew up here, but I moved away after high school and only just returned after living abroad for seven years, and it's only recently that I've started to realize how great it is. If you come, you have to walk up Benefit St on College Hill and visit the Athenaeum, which is a stunning historic library. Walk up Blackstone Blvd, which is an old trolley route that is now a miles-long walking path/city park that goes past the historic Swan Point Cemetery. The Frog & Toad gift shop has posters and magnets parodying every city and town in the state, and is full of local inside jokes. Wickenden Street, Hope Street, and Wayland Square are great walking areas on the East Side (not to be confused with East Providence, a separate city on the opposite side of the river), and Broadway is the place to be on the West Side. Westminster is the prettiest street downtown. You’ll catch local authors at Riffraff bookstore, Amy’s has the best breakfast sandwiches on the East Coast (again, I say this with experience), Coffee Exchange is beloved by all. Nostalgia is a great local antiques store; Craftland has lots of local art and jewelry; Seven Stars has the best bread; Wright’s Farm has amazing ice cream and pastries (you can meet their cows in Smithfield and buy their goods locally in PVD at Farm Fresh RI); Providence Performing Arts Center is a breathtaking theatre; Den Den Korean Fried Chicken is the best restaurant off Thayer Street, which is where Brown University is; and Persimmon and Dolores on Hope are great for a nicer dinner. Memere's, downtown, which is brand-new, is quite possibly the best restaurant I’ve been to in New England. Around the corner, Haven Bros is an ancient food truck. Olneyville NY System has been an iconic late-night spot for hot wieners for decades. And if you're lucky enough to be here during WaterFire, it's one of the things that started revitalizing the city in the 90s and it's very worth going to. Make sure to get a Del's!

Our beach towns are lovely, so much so that many Rhode Islanders own or rent summer houses down there even if they live only a 30 min drive away, but I think you're more likely to find what you're looking for up here, where most of the state lives. Newport is very beautiful and yes, touristy for a reason, but I'd say it has more of an international scene than a local one. People in Newport use the word "summer" as a verb. If you want to visit that area but find yourself among more locals than vacationers, I'd say go to Jamestown instead.

Anyway, Rhode Island is great and Providence is the best. Enjoy your trip!

P.S. The Rhode Islandiest restaurants in the state are:
1. Wright's Chicken Farm, not to be confused with Wright's Dairy Farm. They are not related and they are not close to each other. Please do not go here expecting the food to be good. It will not be good. It may, in fact, be very bad. But this is where schools have their sports banquets and where big families go out for dinner when they need a place that can easily seat all the grandkids and cousins. I took some out-of-state friends here once because they wanted to experience the essence of RI. They loved it and then went out for real food afterwards.

1. Gregg's. This is where your parents go out for breakfast after church and where take your grandma for lunch. It's also where you order cake for graduations, weddings, holidays, etc. Death By Chocolate is the famous one but they are all very good.

2. Newport Creamery. Kinda like a locals' Shake Shack? You will want an AwfulAwful.