Personal opinions:
1. You'll probably want to spend most of your time at the two ends of the trip: Boston and New York.
2. Boston hotels are expensive. (Have you priced rooms large enough for 2 1/2 people at good hotels in London lately?) The only way around that is to stay some distance from the city. You can reach the city easily by public transportation, but depending on your interests and what you want to see, that may take more time than the savings are worth.
3. Many sights in the Boston area are outside the city itself. In contrast to many other cities, the city itself is relatively small. (Not quite as small as the City of London, but much smaller than what people generally think of when they hear London.) Harvard University, for example, is in the city of Cambridge, but if Boston were structured like most cities, it would be in Boston. I'd suggest seeing what you want to see in the central Boston area first, then getting your car - no need to have it for Boston and immediate environs; public transport there is reasonably decent - and doing the day trips.
4. Possible day trips from Boston include Lexington/Concord (where the fighting started when we kicked your ancestors out), the North Shore (attractive cities, waterfronts, etc.) and more. See any guidebook.
5. On your way to New York, I recommend a stop in New Bedford. It's slightly off the direct route but it makes sense to do it while you're driving in that direction. It's the biggest fishing port in the U.S. in terms of landed seafood value, has a real gritty waterfront - not a tourist attraction. While you're there, visit the Whaling Museum. It does a great job of balancing the contribution of whaling to the regional economy 100+ years ago with the more recent recognition of whales' intelligence and their need for protection. If you want to spend a night there, there's a reasonably-priced Fairfield Inn within easy walking distance of the docks.
6. You might consider New Haven, Connecticut, as an intermediate stop. Very historic town, home of Yale University.
7. You probably want to ditch the car as soon as you get to NYC, or if you will need it for day trips in the area, schedule those for the first few days after you get there and ditch it as soon as they're done.
Now let's see what others have to say!