My wife and I are traveling to Boston for a conference this July. We'll have 1 1/2 days to sightsee before the conference and then 2 1/2 afternoons/evenings to explore after the sessions. We'd like to see Cape Cod and maybe Newport. Should we rent a car for the whole trip. We're flying in to Logan and staying in the back bay.

Do not rent a car for the Boston portion of your trip. You will not need it nor will you want to use it and parking is very expensive. The city is fairly compact and walkable, and also has a very efficient public transportation system-www.mbta.com
You'll probably want to rent a car to explore the Cape and or Newport. In addition to the airport, there are numerous car rental agencies located next to the Park Plaza Hotel.

DON'T rent a car while you are in Boston. Rent it only for the days you are leaving the city.

You don't need a car in Boston, and having one will make you very unhappy. Do a search on this site for the multitude of times this question has been asked and answered.

For that amount of time, I would suggest you skip both Newport and the Cape. There is far more than 1 1/2 days of stuff to see in Boston and afternoons/evenings are not long enough to get to and from either other place. I agree, no car.

I agree with everyone else here, do NOT rent a car in Boston. If you need to rent one for one day while you go on a day trip, that would be fine.