Your post caught my attention because I'm a native New Englander and never saw Rhode Island pluralized. Not to be picky at you but the official name is the State of Rhode Island and Providence Plantations. Anywho, I'm assuming you are taking the Great American Waterways cruise which ends in Warren, RI.
Depending on how long you are staying in the area following the cruise, you may be able to cover a lot of territory. RI may be small but it is full of great destinations and because it is so small, none of them take very long to get to!.
Newport, RI - Beautiful waterfront area to explore, nice public beach, the mansions, Tennis Hall of Fame, Yachting Museum, numerous farms and wineries. We have been to many of the attractions on this page: http://www.discovernewport.org/attractions and would not regret returning to them either. Not all are in Newport proper but like I said, it's a small state.
Providence, RI - Providence is the capital city. It is laid out in neighborhoods, a bit hilly in places, but easy to reconnoiter. Depending on your schedule, Fire Water is a unique take. If you are a foodie, there are lots of choices for great places to nosh. The college area offers an interesting mix of museums, shops, bistros, etc. We have always enjoyed the atmosphere there.
If you care to venture a bit outside of RI, Connecticut is not too far. Gambling types will enjoy either Foxwoods or Mohegan Sun, the two most established casinos in the region.
That will get you started. Have an ab fab vacation, and please come back to post a review of your trip.