You will have about 80% of what you need within walking distance. Plenty of restaurants, tours, docks, shopping around. But, for the mansions, cliff walk, beaches, fort adams and a possible grocery run, I would suggest a car for. If you don't want to rent a car, you could always uber or there is a zip car lot very close to Long Wharf.
Not that you asked....but there are a couple groupons for Newport I just picked up that may interest you.
$25 for a $50 Ryan Amusements gift card. If you are traveling with kids that like to play games to win tickets and redeem them for well....junk, Ryan has an arcade in Newport for this.
$38 for a soap making class for 2. Also within walking distance. They run I think on Monday and Wednesday nights (double check that) and you can BYOB.