RIPTA is a great way to get around all of rhode island if you do not have a car. You can travel anywhere in the state for $1.50. The other day I had my bike (bike racks are in front of the bus), and went from Newport to Providence for just $1.50 (even cheaper than driving). Buses could take significantly longer than driving, depending on number of stops. There are also other ways to go, such as the providence-newport ferry.
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