We are New Englanders and it was nice to vacation near home. Newport has some great attractions, with the beautiful mansions maintained by the Preservation Society of Newport County (don't be put off, even with children--our 6-year-old son had a great time). The Cliff Walk is fun and great exercise--finish it off with a sundae at the Newport Creamery in the center of town. There is some shopping in the waterfront area, but not so much as to distract or overindulge.
The scenery on the outskirts of town and in Jamestown (where we stayed, on the other side of Narragansett Bay) is some of most beautiful coastline we've seen in New England. The best public beaches for bathing are in Middletown (Second and Third Beaches), though Mackeral Cove in Jamestown was very nice.
Beavertail State Park and Lighthouse in Jamestown is spectacular. Other interesting sites on Conanicut Island include Watson Farm, with its cattle, sheep, horses, gardens, and miles of picturesque trails; Forts Wetherill and Getty (now recreational areas); and the Conanicut Island Bird Sanctuary.