New York City is the worst example of an American city you could have chosen. Because it's bounded by water on all sides, it's the one American city that has developed in an extremely dense manner and is thus walkable. You are right for essentially any other American city, though.
Yeah, a lot of people visiting NYC never leave a relatively small area of Manhattan. I don't mind walking relatively long distances (and I'm fine with taking the NYC subway) but on my typical NYC visit I never use anything other than my feet to get around. The same is somewhat true of London though I'm more likely to get on the tube there.
Added: It depends too on where you're going in the city. There are a fair number of US cities where walking works fine so long as you restrict your travel mostly to the city core, which people often do on a short trip.
Perhaps I'm being a little pedantic here, but NYC is not bounded on all sides by water - the Bronx is part of mainland NYS. But yes - for the most part NYC is geographically constrained.
