Definitely visit the obvious things like the mansions and Ocean Drive, Fort Adams (even though in 3 months we never got there!) and if you have a car and like shopping, go to Providence -- Providence Place Mall is 4 floors of heaven!
Quick Tips:
If you collect Nantucket baskets, Shrimshaw, or anything collectible really, check out Newport Trading Company, 170 Thames Street, up near Brick Alley pub -- ask for Mike or Joe. I worked with them for the summer and they're lovely people!Best Way To Get Around:
We either walked or got the bus everywhere for 3 months and we managed fine! The Ripta Trolley are very for going to the beach