The Roger Williams Park is a beautiful place for a run. With sidewalks alongside nearly the entire run, there are only a couple of high-traffic areas (unless you count the geese). Despite these few places, this route can basically be done in the middle of the road.
This 3.12 mile loop runs past the Temple to Music, and The Roger Williams Botanical Gardens. If you’re up for an extra 2 miles (approximately), you can follow Vendale Ave (which will become Natural History Ave), and run past the Natural History Museum. At the rotary, turn onto Green Memorial Blvd, past Betsy Williams College. This will loop you around, right back to the Roger Williams Park Carousel.
Starting at the Carousel is recommended due to ample parking. If you’re staying in the downtown area, this route is accessible via bus 40 — Butler Hospital. Board at Tunnel FS Thayer stop, until Rochambeau NS Blackstone.