The foot is the best way to get around town and see things. It is a wonderful town to just stroll around and see what you can find. Around each corner will always lead to something you have never seen before.
My wife and I usually stay at the Hyatt, The Hotel Viking or one of the centrally located B&B's in Newport which makes walking around the downtown area rather easy.
Walking around can be difficult during the winter months as they do not shovel as well as they should for pedestrians. My wife and I were in Newport several times during winter 2015 and some sidewalks were simply unwalkable for the tremendous amounts of snow and ice on the pavement.
I spend a lot of time exploring a location walking around at my leisure. I park my car usually at that Visitor's Center and walk America's Cup Ave to the wharfs and around the waterfront.
I love walking because it allows me the freedom to stop for something to eat or drink, peruse a store, do some shopping, wander with no worries about where to park the car or that the time on the meter is up.