I went to school in Providence and regularly visit my brothers there. It you want to see New England you may be interested in what it offers. Providence itself it a very walkable city from College Hill to Federal Hill. Amtrak Station is on Gaspee Street across from the State House. Providence Place is a shopping center one block away with any kind of store you need and a food court.
The Providence Arcade, the nation's first shopping center, is a pleasant place to stop for lunch and has may small shops. The Providence Library on Empire Street offers Rhode Island history and just a place to sit down and rest a while. In the other direction on College Hill are a lot of restored colonial homes as well as the First Baptist Church founded by Roger Williams. Up the hill you will find the John Brown House. Brown was a slave trader and the wealthiest man in the state at the time of the Revolution. He endowed Brown University.
Rhode Island has an extensive bus system, RIPTA, located on Kennedy Plaza, a 10 minute walk out the back of the Station or you can catch a bus on Gaspee Street. There is regular bus service to Newport, the most famous place to visit with tours of mansions from the Gilded Age. The Breakers and the Marble House, both owned by different members of the Vanderbilt Family are there along with a number of others. In Pawtucket, also easy to get to is the original spinning mill Moses Brown (John's Brother) built for Samuel Slater. This was the start of the industrial revolution in America. One of Slater's mills was located in Woonsocket, RI. The workers were mostly Canadian French people from Quebec. Today the Museum of Work and Culture describes their history. And there are other institutions with information about French Canadians in the state. There are buses to Woonsocket but they are infrequent; you may prefer to rent a car. If you can get to Quonset Point below East Greenwich you will find a Seabee Museum which includes displays of Quonset Huts. If if were summer I would talk about Rhode Island beaches but it is a little cold for them right now.
This is a run down off of the top of my head. If you have time Rhode Island published an excellent and free state map. You can order one on the state website. Have a good trip wherever you go.