I was in Rhode Island a few months ago and loved there with my cousins. If you have kids, things to do include visiting the Whaling National Historic Park. enjoy time at Newport beach, visit the Rhode Island School of Design Museum, attend the St. Patrick's Day weekend (in March), and visit the planetarium at the Natural History Museum (located in Roger Williams Park). Hope this helps
Re: things to do with family in Rhode Island In the summer, there's nothing better to do in Rhode Island than heading to one of the quieter beaches of the state like Blue Shutters Beach or Charlestown Town Beach. Eating out is great too at Captain Jack's or Jim's Dock in Matunuck. Visit also Watch Hill village in Westerly for the antique carousel (kids who grab brass ring get a free ride).
The Providence Rink at the Bank of America City Center is a cool place to go with the family for a nice day out. There's also a regular events that you can attend like the WaterFire Providence which is a series of bonfires installed on the three rivers of downtown Providence. The event occurs several times a month from May to November