Having a car in Boston is a liability, but I think I'd rent a car to get to Newport. Parking's somewhat easier in Newport (except for Thames St).
You don't need a car in Boston, because you either just walk or take the T (subway). "Buy" a Charlie card at a T stop (you don't pay extra for the card, you just pay for the rides). All the rides cost the same, whether you only go one stop or go to the end of the line. Each neighborhood has a really different feel
pr character--a bit like San Francisco, I suppose.
Back Bay (Newbury St and Boylston) is trendy. Great for walking and shopping, but not really any stand out restaurants I'd recommend.
North End is traditional Italian. Hard to find a bad restaurant there. I like Giacomo's. Artu is another favorite. Strega is trendy. I'm sure other Bostonians have their favorites. Just remember that a lot of restaurants only take cash. After dinner, head back to Hanover St (the main drag) for canolis and espresso at either Mike's or Modern Pasrty.
Faneuil Hall and Haymaket are popular touristy areas. Street performers, touristy trinkets, some shopping, restaurants and food court. The Aquarium is really nice. There's also the Museum of Modern Art (MOMA).
The Fen has Fenway Park. If you can squeeze in a Red Sox game, it's a treat, even if you're not a hard core baseball fan.
Beacon Hill (main drag, Charles St) is historic old-money Boston. Super beautiful and picturesque neighborhood. Acorn Street is an alley which is the most-photographed street in Boston. If you're on Charles St on a Friday summer afternoon, it's neat to see waves of young people walking down from Beacon Hill to go to restaurants and bars.
Cambridge doesn't just have Harvard (where you can take a free guided tour). There's also shopping in Harvard Square. My daughter took is to a hole-in-the-wall Indian place, Singh's Dhaba, which was really good.
The Seaport area has really exploded in popularity over the past 20 years. Shops, restaurants, and an F1-themed bar where you can sim race.
Boston has really good Thai food. Brown Sugar and Bangkok Bistro in Brighton were favorites. Carlo's in Brighton is also North End quality Italian (but in Brighton).
If it's rainy, there are interconnected mall complexes (Copley, the Prudential) where there's shopping and dining.
If you're into history and sightseeing, you can take a Duck Tour. They leave from different places (Science Museum, the Pru, and the Aquarium). It's in one of those amphibious WWII landing craft, and they take a ride into the Charles River. Quality of the tour depends on the tour guide, though. Ther's also the Freedom Trail. It's a self-guided tour that winds through Boston. It takes you to many of the historic places (Betsey Ross' house, Paul Revere's house, Old North Chirch, USS Constitution, etc). It's denoted by a red line painted (or bricks) on the ground.