NY, Boston, and DC are three of the best cities in the US for public transit, with NY the clear leader even though the locals complain relentlessly about the sad state of the system (it has its share of failures like the tube).

How to spend your time really depends on what type of tourist you are. There's easily enough in each of these three cities to keep me interested for 2-3 weeks, but some just like to see the big sights, have a few nice meals, and move on to something else. Whereas I tend to prefer at least a week in any city I visit (and for example would want at least two weeks in Florence or Rome, a month in Paris, etc.).

As others have noted, DC and NY will be quite warm usually that time of year which is the only thing inhibiting walkability (I tend to counter this by getting up early and staying up late and taking a break in the middle of the day), and Boston could be as well or could be rather pleasant.