Cranston - Sprague Mansion - haunted by numerous ghosts in various rooms.

Narragansett - Old Wedderburn House - the ghost of a small woman in a black veil haunts this house.

Newport - Porter Mansion - Richard Washburn Child haunts this building in which he died.

Newport - Belcourt Castle - There is  a statue of a monk in the chapel of the castle.
Before it was placed in the chapel, it was near the stairs.  A person going through the house would sometimes see a man dressed as a monk near the stairs.  He hasn't been seen since he was moved to the chapel.

North Kingstown - Scallabrini Villa -   haunted by the ghosts of children that have died there.  It is presently a nursing establishment composed of two building facilities.  The new building  was erected in 1995.  However the older building completed way back, unsure of the date, was originally a Rhode Island Hospital children's facility.  It is said that children could be heard laughing, crying, or playing.  Particularly, rm 103 is said to be the room where many spirits stay.   Keep in mind that it presently houses retired nuns and priests, and is under direction of the Scallabrini Fathers, so you may not be able to gain access.  Still, i think it's at least worth the question.

Providence - College Hill - The ghost of H.P. Lovecraft, author, is said to haunt several sites on College Hill.  He taught at one of the colleges and his ghost is said to roam the halls there.   Lovecraft based the towns and colleges in his stories on the places he knew around New England.

Newport - The Astors' Beechwood mansion - Candles blowing out by themselves and foot steps on a secret stair case.   Strange images and sounds.  Cold spots and just "knowing" that someone was watching you.

Cumberland - Wets Wrentham Colonial House - Haunted by an old man who appears in dreams, makes rapping noises, makes appearances, and  creates strange noises.

Newport - Salve Regina University - Several dormatories and the Wakehurst Student Center have  many stories about them, names being called. Carey Mansion, supposedly a nun hung herself.  the room is boarded up and every month a priest  has to come in and bless the house.  All ouiji boards are banned from the house because of inexplainable "situations"....

Warwick -  The Aldrich Mansion - supposedly one of the Aldrich daughters killed herself by jumping off a balcony.   There have been some sightings there by employees.

Bristol-Roger Williams University Theatre   'The Barn'-
Originally two separate 19th century barns the Roger Williams theatre is home to a ghost sometimes referred to by the students as Banquo.  I was told that a farm hand froze to death in the hayloft of one of the barns before it was the theatre.  There have been accounts of cold spots where the temperature is significantly colder in a localized area.  Also of the heavy stage 'blacks' blowing in the wind when there is no wind.   Names being called by no one.

Newport-Belcourt Castle-
Many unusual ghosts. 1- 2 Chairs in the Gothic Ballroom have spirits in them. Put your hand near the chairs, your hand gets cold and prickly, try to sit in one, there is resistance, try to sit in the other, it might throw you out.    2- there is an armor in the Gothic ballroom who’s owner died when a spear went through the eyeslot and out the other end. He can be heard screaming in and around March.

Providence-Johnson and Wales University-
A dormitory that used to be a monastery is supposedly haunted by a nun that went crazy nearly 60 years ago. She is seen walking on all the floors late at night.  Also one of the rooms on the second floor has walls that bleed.

Providence-Xavier Hall (Johnson and Wales).-
Formerly St. Xavier Rectory Students have reported furniture moving in their dorm rooms.   Some have felt tremendous cold feelings and almost audible anger coming from some rooms.  This has not been documented, but it seems that a nun may have been murdered by a priest there at some time.

Bristol-Colt School-
It is said to be haunted by the ghosts of the family that have their pictures in the auditorium. In the boys bathroom strange smells and voices are heard and at night you can sometimes see ghosts wondering the halls.

Newport-Bretton Point-
There is an old, abandoned stable and widow's walk on a tower top in the back of the "kite-flying" field.  There are noises and voices such as banging, horse trotting, and conversations.    Many people have experienced a wide variety of phenomenon.

Kingston-University of Rhode Island-Theta Delta Chi Fraternity-
A ghost named Barbara haunts the third floor of this building.  Her child has been seen bouncing a ball down the main aisle of the third floor sleeping decks.